On the asymptotic number of non-equivalent q-ary linear codes

被引:4
作者
Hou, XD [1 ]
机构
[1] Univ S Florida, Dept Math, Tampa, FL 33620 USA
关键词
asymptotic; invariant subspace; q-ary linear codes; the symmetric group; wreath product;
D O I
10.1016/j.jcta.2005.08.001
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let M-n,M-q subset of GL(n, F-q) be the group of monomial matrices, i.e., the group generated by all permutation matrices and diagonal matrices in GL(n, F-q). The group M-n,M-q acts on the set V(F-q(n)) of all subspaces of H. The number of orbits of this action, denoted by N-n,N-q, is the number of non-equivalent linear codes in F-q(n). It was conjectured by Lax that N-n,N-q similar to vertical bar V(F-q(n))vertical bar/n!(q - 1)(n-1) as n -> infinity. We confirm this conjecture in this paper. (c) 2005 Elsevier Inc. All rights reserved.
引用
收藏
页码:337 / 346
页数:10
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