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Linear size optimal q-ary constant-weight codes and constant-composition codes.

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Linear size optimal q-ary constant-weight codes and constant-composition codes.

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Title: Linear size optimal q-ary constant-weight codes and constant-composition codes.
Author: Chee, Yeow Meng.; Dau, Son Hoang.; Ling, Alan C. H.; Ling, San.
Copyright year: 2009
Abstract: An optimal constant-composition or constant-weight code of weight w has linear size if and only if its distance d is at least 2w-1. When d ≥ 2w, the determination of the exact size of such a constant-composition or constant-weight code is trivial, but the case of d=2w-1 has been solved previously only for binary and ternary constant-composition and constant-weight codes, and for some sporadic instances. This paper provides a construction for quasicyclic optimal constant-composition and constant-weight codes of weight w and distance 2w-1 based on a new generalization of difference triangle sets. As a result, the sizes of optimal constant-composition codes and optimal constant-weight codes of weight w and distance 2w-1 are determined for all such codes of sufficiently large lengths. This solves an open problem of Etzion. The sizes of optimal constant-composition codes of weight w and distance 2w-1 are also determined for all w ≤ 6, except in two cases.
Subject: DRNTU::Science::Mathematics.
Type: Journal Article
Series/ Journal Title: IEEE transactions on information theory
School: School of Physical and Mathematical Sciences
Rights: © 2009 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The published version is available at: http://dx.doi.org/10.1109/TIT.2009.2034814.
Version: Accepted version

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