摘要
Wolfmann引进了 Z4-负循环码 .Zn4 上的负移位γ是指 Zn4上的满足γ( a0 ,a1 ,… ,an- 1 ) =( - an- 1 ,a0 ,a1 ,… ,an- 2 )的置换 ;长度为 n的 Z4-负循环是指 Zn4的子集 C满足γ( C) =C.他给出了在环 Z4[x]/( x2 + 1 )中多项式表示的 Z4-负循环码 ;证明了 Z4-线性负循环码 Gray映射下的象是二元距离不变量循环码等 .本文有两个目的 :一是给出在环 Z2 k[x]/( x2 + 1 )中的多项式表示的 Z2 k-负循环码及其对偶 ;二是由 Z4-负循环码在 Gray映射下的象构造出具有优良关连性质的二元周期序列族 .
Wolfmann introduced negacyclic codes over Z_4. The negashift γof Z^n_4 is defined as the permutation of Z^n_4 such that γ(a_0,a_1,\:,a_(n-1))=(-a_(n-1),a_0,a_1,\:,a_(n-2)) and a negacyclic code of length n over Z_4 is defined as a subset C of Z^n_4 Such that γ(C)=C. Wolfmann produced negacyclic Z_4～codes by ploynomial represent in the ring Z_4[x]/(x^2+1),and proved that the Gray image of a linear negacyclic code over Z_4 of length n is a binary distance invariant cyclic code. The purpose of this paper is twofold. First, negacyclic Z_(2~k)～codes by polynomial represent is the ring Z_(2~k)[x]/(x^2+1) and their dual are produced. Second, binary periodic sequences with good correlation properties from negacyclic Z_4～code via Gray map are constructed.
出处
《纯粹数学与应用数学》
CSCD
2004年第3期219-224,共6页
Pure and Applied Mathematics
基金
安徽省教育厅科研基金资助 ( 2 0 0 4kj2 71)
