Nonequivalent q-ary perfect codes

被引：6
|
作者：
Etzion, T
机构：
[1] Computer Science Department, Royal Holloway, University of London, Egham
[2] Computer Science Department, Technion - Israel Inst. of Technol.
来源：
SIAM JOURNAL ON DISCRETE MATHEMATICS | 1996年 / 9卷 / 03期
关键词：
Hamming codes; isomorphism; nonequivalent codes; perfect codes;
D O I：
10.1137/S0895480194277903
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We construct a set of q(qcn) nonequivalent q-ary perfect single error-correcting codes of length n over GF(q) for sufficiently large n and a constant c = 1/q - epsilon. The construction is based on a small subcode A of the q-ary Hamming code of length n for which A and q - 1 of its cosets A(1),..., A(q-1) cover the same subset V. We show a few isomorphic and nonisomorphic ways in which A can be chosen, and we prove the uniqueness of these ways to choose A.
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页码：413 / 423
页数：11
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