The History of MinT

This is a list of the most recent additions to the MinT database. Some minor changes may be omitted.

2008-03-11 Nets constructed from net-embeddable BCH codes by Ling and Özbudak.
2008-02-25 Construction XX for (not necessarily narrow-sense) BCH codes.
2008-02-14 Quaternary quasi-twisted codes of dimension 6 by Gulliver and Östergård.
Another tower of algebraic function fields by García and Stichtenoth.
Caps in AG(6,3) have at most 112 points.
2008-01-11 Information about the Weierstrass semigroup of the Klein function field. Algebraic-geometric codes and NRT-codes defined using a non-rational place. Standard lengthening for algebraic-geometric NRT-codes in cases where non-rational places or information about the Weierstrass semigroup are used.
2008-01-03 Exploiting information about the Weierstrass semigroup of the Hermitian and Suzuki function fields give the true parameters of Hermitian and Suzuki codes.
2007-12-21 Construction X4. Construction X and related propagation rules are applied to the non-linear orthogonal arrays from Kerdock and Delsarte–Goethals codes.
New codes by Kohnert and Zwanzger and Gashkov and Sidelʹnikov.
Nets constructed from net-embeddable BCH codes by Helleseth, Kløve, and Levenshtein.
2007-12-03 Construction XX and Construction XX applied to a chain of subcodes. Construction X (and construction XX) applied to chains of extended narrow-sense BCH codes.
2007-11-21 The general Roos bound is applied to all cyclic codes with length s ≤ 40; the simple Roos bound to all cyclic codes with length s ≤ 60; and the BCH bound to all cyclic codes with length s ≤ 100. Construction X is used for all subcode pairs of these cyclic codes. The parameter range for narrow-sense BCH codes and arbitrary BCH codes has been increased. Contraction of cyclic codes.
Many additional linear programming bounds for orthogonal arrays with 150 < s ≤ 300 have been calculated.
2007-10-10 Codes by Kohnert and Zwanzger.
Information for bases b = 64, 128, 256, and 81 (and additional information for bases b = 8 and 49) is included, which yields many new results for lower powers of 2, 3, and 7.
2007-09-27 Simple Roos bound and general Roos bound for narrow-sense BCH codes. BCH bound for non-narrow-sense BCH codes.
Codes by Danev and Olsson. Codes by de Boer and Brouwer including construction X applied to these codes.
Base reduction for projective spaces, used for orthogonal arrays as well as nets.
A bound by Trinker derived from the LP bound for OOAs.
2007-08-08 Nets defined by OOAs with a strength at least as large as the depth.
Discarding parts of the base for OAs and OOAs.
More propagation rules for OOAs: concatenation of two OOAs, concatenation of two NRT-codes, base expansion for OOAs, construction X for NRT-codes based on algebraic-geometric NRT-codes and OOAs from (ts)-sequences. Gilbert–Varšamov bound for OOAs, including nets obtained by Gilbert–Varšamov-embedding of OOAs.
Some constructions for codes with low dimension: Denniston codes, codes from dual arcs, and codes of Belov type.
Information about base b = 49 is included, which yields many new results in base b = 7.
2007-06-28 Many linear programming bounds for orthogonal arrays with 150 < s ≤ 300 have been calculated. Furthermore, some linear programming bounds for OOAs in depth T = 4 are included, proving (amongst other things) the nonexistence of (3,7)-sequences in base b = 2.
A (6,14,15)-, (10,20,21)-, (12,17,142)-, (14,19,278)-, (16,21,542)-, (18,23,1068)-, and a (20,25,2110)-net in base 2 obtained from a computer search for net-embeddings of linear OAs by Edel. In cases where the OA is not net-embeddable, generator matrices for OOAs in depth T = 2 are obtained.
A construction for ternary caps by Edel. Two classes of projective codes by Bierbrauer and Gulliver over F9. The projective code obtained from the ovoid and Construction X applied to this code and its one-dimensional subcode.
Cyclic, quasi-cyclic and quasi-twisted codes by Bierbrauer and Gulliver, Daskalov and Gulliver, Gulliver and Bhargava, Boukliev, Boukliev, Daskalov, and Kapralov, and Daskalov, Hristov, and Metodieva.
Many new explicit generator matrices for linear codes.
Nonexistence of linear codes obtained using the linear programming bound with additional knowledge about impossible weights. Nonexistence results for codes by Hill and Landjev, Landjev, Maruta, and Hill, Hill, and Boukliev, Kapralov, Maruta, and Fukui.
2007-05-31 OOAs extracted from nets.
Upper bounds on the size of affine caps (used for establishing bounds on the size of projective caps) are included as independent objects: Trivial bound, optimality of the affine subcap of ovoids, other sporadic bounds, a recursive formula by Bierbrauer and Edel, base reduction, and embedding an affine cap in projective space.
2007-05-14 The parameter range considered by MinT has been expanded up to m ≤ 260 for bases b = 2 and 4; up to m ≤ 250 for base b = 3; up to m ≤ 150 for bases b = 5, 8, and 9; and up to m ≤ 130 for base b = 16.
Johnson bound and improved Johnson bound.
BCH codes: All narrow-sense BCH codes are included with their true dimension and their minimum distance bounded by the BCH bound considering all possible intervals (for s ≤ 10000) or only some common classes of intervals (for s > 10000). Construction X is applied in all possible situations.
Projective codes obtained as a union of disjoint Baer subplanes.
Constructive function fields by Sémirat, some of them containing places of degree 2.
2007-03-31 The functionality provided by the MinT database has been improved considerably:
  • Information about ordered orthogonal arrays (OOAs) with various depths is included, expanding the special cases of orthogonal arrays (depth T = 1) and nets (depth T → ∞), which were available before.
  • Non-existence results for (tms)-nets and (ts)-sequences are derived from appropriate results for OAs and OOAs.
  • Tables and detailed results can be generated for all 38 reasonable choices of two independent and one depending variable from the six variables t, m, s, k, d, and n.
  • In addition to an advanced interface providing access to all possible queries, simplified interfaces for nets, linear codes, and orthogonal arrays are provided.
  • MinT can now handle propagation rules with more than two parents.
  • MinT can now handle propagation rules based on both an existence and a non-existence result.
  • Additional information about how a certain method has to be applied in oder to obtain a result is provided.
  • MinT distinguishes between algebraic function fields with exactly known genus and fields where only an upper bound on the genus is available.
  • A glossary providing definitions of important objects used by MinT is provided.
Bounds for OOAs: Rao bound, Plotkin bound, Singleton bound, linear programming bound, and linear programming bound with quadratic polynomials
Constructions of OOAs: OOA with only one run, arbitrary OOA, complete OOA, repetition NRT-code, Reed–Solomon NRT-codes, and algebraic-geometric NRT-codes
Propagation rules for OOAs: strength reduction, discarding factors, embedding NRT-code in larger space, duplication, NRT-code trunctation, m-reduction, NRT-code repetition, NRT-code juxtaposition, trace code, direct product, (uu+v)-construction, depth reduction, extracting OOA from net, increasing depth to T > k, increasing depth from T = k−1 to T = k, embeddability of OAs with strength k = 3, folding, folding and stacking, folding and stacking with additional row, and stacking with additional row
2007-02-14 We have calculated almost all LP-bounds for OOAs for depth T = 2 with k ≤ 15 and s ≤ 35 (in addition to the bounds with s ≤ 25). Furthermore almost all bounds for depth T = 3 with s ≤ 11 and with k ≤ 20 and s ≤ 15.
Some possible applications of the propagation rules code truncation (for codes and OAs) and base change (for nets) were missing.
2006-12-20 We have calculated all LP-bounds for OOAs for depth T = 2 with s ≤ 25 and with b = 2, k ≤ 14, and s ≤ 35.
2006-11-29 New function fields from the November 2006 edition of van der Geer and van der Vlugt’s list of curves are included, but do not yield new codes or sequences.
2006-11-10 Towers of function fields by van der Geer and van der Vlugt, Bezerra, García, and Stichtenoth, Bezerra and García, and by García, Stichtenoth, and Rück.
Niederreiter–Xing sequence III with García–Stichtenoth tower over F49 yields many sequences over F7.
A function field with places of degree two over F5 by Mayor and Niederreiter.
2006-10-25 (Extended) quadratic residue codes.
Some codes with given generator matrix: A [15,6,7]- and [16,5,9]-code over F3 and a [18,9,8]-code over F4. Some cyclic codes with given generator: [31,11,11]-, [33,13,10]- and [43,15,13]-codes over F2.
Bound for linear codes by Fontaine and Peterson.
All shift nets from Schürer’s PhD thesis are included.
2006-10-01 Many additional LP bounds for OAs have been included. Currently we have calculated all bounds for s ≤ 150 for all bases.
2006-07-11 Some codes: The unital, codes by Marcugini, Milani, and Pambianco, and codes by Bierbrauer, Marcugini, and Pambianco.
2006-07-04 Many results about shift nets have been included. In particular there are many new nets for b = 2 and b = 3.
2006-06-24 Many LP bounds for OAs have been included in the database. Currently we have calculated all bounds for s ≤ 133 for b = 2, 3; up to s ≤ 132 for b ≤ 4; up to s ≤ 122 for b ≤ 5; and up to s ≤ 100 for b = 7, 8, 9, 16, 25, 27, and 32.
2006-03-21 A number of algebraic function fields over ℤ7 and F25 were discovered by Yeo and Teo.
2006-03-10 Varšamov–Edel lengthening.
Codes constructed by Edel by Inverting Construction Y1.
2006-02-26 Construction Y1 is applied in all three possible directions.
2006-02-23 Information about near-MDS codes: A [12,4,8]-code over F5, the dual code of a near-MDS code is again a near-MDS code, and the non-existence of [13,5,8]- and [12,5,7]-codes over F5.
Affine sub-caps of PG(5,b) with b > 9. See here.
2006-02-21 Additional data from Brouwer’s database.
2006-02-07 Generalized (uu+v)-construction.
2006-01-30 New function fields from the January 2006 version of van der Geer and van der Vlugt’s list of curves included.
2006-01-23 (uuvu+v+w)-construction.
2006-01-17 Algebraic function fields by Beelen and Pellikaan, Keller, Auer, and the Suzuki curve.
Additional Drinfelʹd Modules of Rank 1 by Niederreiter and Xing.
A propagation rule for linear codes based on algebraic function fields by Niederreiter and Xing (obsolete).
2006-01-11 A bound for OOAs derived by Bierbrauer from the Linear Programming bound based on quadratic polynomials.
2005-10-18 A construction for caps based on two projective caps and one affine cap avoiding two hyperplanes.
2005-10-11 Martin and Visentin were able to show that the (dual) Plotkin bound for OOAs is also applicable to not necessarily linear OOAs.
2005-10-10 New function fields from the September 2005 version of van der Geer and van der Vlugt’s list of curves included.
Function field from Klein quartic over F8.
Bounds on the length of MDS-codes.
Information about almost-MDS codes: plane (s,3)-arcs in PG(2,b) by Ball, a construction for [ss−6, 6]-codes from [s, 3, s−3]-codes by de Boer, and bounds by de Boer and Thas and Barlotti.
With the help of Yves Edel a lot of information about caps (i.e., [sn, 4]-codes) has been included in MinT: Caps by Hill, Glynn, and Tallini (optimality) as well as (hyper)ovals. Large caps in PG(4, b), PG(5, b), and computer completed caps. Caps constructed as products of two caps with tangent hyperplanes, of a projective and an affine cap (with trivial AG(2,b)-cap or other affine caps), and of two projective and one affine cap avoiding two hyperplanes (with trivial AG(2,b)-cap, (hyper)oval, or other cap). Bounds on the size of caps by Pellegrino, Barlotti, Hirschfeld, and Thas, Edel, Storme, and Sziklai, Gronchi and Heim, and Barát, Edel, Hill, and Storme. Furthermore bounds based on the size of affine caps and cap doubling and removing affine subspaces and bounds obtained from Hill recurrence.
2005-07-20 (Dual) Plotkin bound for OOAs applied to sequences.
Additional data from Brouwer’s database.
2005-06-15 Trivial code.
2005-05-08 Van der Corput sequence.
2005-04-13 (Dual) Plotkin bound for OOAs.
2005-03-20 OOAs of depth 2 which are net-embeddable by the Gilbert–Varšamov bound by Bierbrauer and Edel.
Nets constructed by embedding BCH codes by Bierbrauer and Edel.
2005-03-04 Construction X4 with Kerdock OAs.
Sharpened Johnson bound.
2005-02-14 Two function fields with a place of degree two over F5 by Niederreiter and Xing.
2005-02-03 Base change for nets.
2005-01-25 Algebraic function fields by García and Quoos .
Towers of algebraic function fields by García and Stichtenoth and with intermediate fields by Niederreiter and Xing.
Exact formulas for the number of rational places of function fields with genus 1, genus 2, and genus 3.
Algebraic-geometric codes and Construction X based on such codes.
2005-01-17 Algebraic function fields are listed as independent objects in MinT.
Rational function field, Hermitian function field, and various other explicit function fields.
Algebraic function fields by Niederreiter and Xing over F3, F4 (not used), F5, and F9. Drinfelʹd Modules of Rank 1 by the same authors.
List of algebraic function fields by van der Geer and van der Vlugt and by Niederreiter and Xing.
2005-01-03 Quaternary constacyclic codes with minimum distance 5.
2004-12-30 Kerdock, Preparata, and Delsarte–Goethals codes.
2004-12-20 Construction Y1 (bounds only).
Salzburg tables.
All parameters of linear codes established in the articles of Edel have been included in MinT: Explicit generator matrices, extended or lengthened BCH codes, extended or lengthened subfield codes of Reed–Solomon codes, codes obtained from BCH codes, concatenation and construction X, linear codes obtained from additive codes and concatenation, BCH codes lengthened with UEP codes, codes constructed by inverting construction Y1, and the codes from Edel’s PhD thesis (obsolete).
2004-12-13 Ovoids (and their optimality), the Tetra code, the ternary (extended) Golay code, and some codes with explicit generator matrix.
Reed–Muller codes.
The dual code of an MDS-code is again an MDS-code. Adding a parity check bit is also valid for non-linear OAs.
Construction X based on Reed–Solomon codes and on the Varšamov bound.
Bounds for OAs with index unity and the Bose–Bush bound for OAs with strength k = 3.
2004-11-30 Linear Programming bound for OOAs by Martin and Stinson.
The binary (extended) Golay code and the Nordstrom–Robinson code.
Simplex codes and (Extended) Reed–Solomon codes.
A bound for OAs by Simonis.
Juxtaposition and concatenation of two codes. Repeating each code word and residual codes.

Early History

Unfortunately details about the earlier history of MinT are lost in the mists of time. Therefore we only list some milestones of the origin of MinT:

The beginning of MinT was probably a meeting on February 27, 2004 between Wolfgang Schmid, Rudolf Schürer, Kristijan Mihalic (who would write the prototype of the front end), and Bernhard Hechenleitner (at that time in charge of the web server). The design and development of MinT started in March 2004. The very first access to a page that would eventually become MinT was on March 8, 2004 14:30:52 MET (according to Apache’s log file).

The first real data set was prepared on March 11 by Rudolf Schürer. It included the trivial lower bound on t and the bound for strength k = 2 (but applied directly to nets); trivial nets, nets with strength k = 1, nets from the Sobolʹ and the Niederreiter sequence using the implementation of Bratley, Fox, and Niederreiter, nets from the Niederreiter–Xing Sequence as implemented by Pirsic, and shift nets; Sobolʹ, Niederreiter, and Faure sequences; as well as the propagation rules m-reduction, s-reduction, t-expansion, and net from sequence.

MinT has been available at the address since September 21, 2004. The first public presentation of MinT was Rudolf Schürer’s talk MinT – A web based database for querying optimal (tms)-net parameters at the conference “Number theoretic algorithms and related topics” in Strobl, Austria on September 27, 2004.