Contraction
Let C(A) denote a cyclic [s, n, d]-code over Fb and u ≥ 2 an integer such that u | b−1, u | s, and all elements of B := – (ℤs ∖ Aʹ) have the same remainder mod u. Then d must be a multiple of u and the projection of C(A) on its first s/u coordinates is a constacyclic [s/u, n, d /u]-code, the so called contraction of C(A).
See Also
[1, Section 13.4]
References
| [1] | Jürgen Bierbrauer. Introduction to Coding Theory. Discrete Mathematics and its Applications. Chapman & Hall/CRC, Boca Raton, London, New York, Washington D.C., 2004. MR2079734 (2005f:94001) |
Copyright
Copyright © 2004, 2005, 2006, 2007, 2008, 2009, 2010 by Rudolf Schürer and Wolfgang Ch. Schmid.
Cite this as: Rudolf Schürer and Wolfgang Ch. Schmid. “Contraction.”
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Version: 2024-09-05.
http://mint.sbg.ac.at/desc_CContraction.html