Quasi-cyclic codes with cyclic constituent codes
Quasi-cyclic codes with cyclic constituent codes
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DOI：
10.1016/j.ffa.2005.11.006
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发表时间：
2007-07
期刊：
影响因子：
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通讯作者：
C. J. Lim
中科院分区：
文献类型：
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作者：
C. J. Lim
Ling和Solé[S.Ling，P.Solé，关于拟循环码的代数结构I：有限域，IEEE译.通知我。理论47(2001)2751-2760]证明了每个拟循环码C都是由称为C的构成码的较短线性码构成的，给定一个长度为ℓm、索引为ℓ的拟循环码C，其中m与ℓ成对互素，且域C的阶已结束，如果它的所有构成码都是循环的，且其零点具有全重数，则C等价于循环码，其零点及其重数可用循环构成码的非零点完全刻画.文中还给出了获得上述等价循环码的一般变换。这里采用的方法遵循了A.M.A.Nativida[A.M.A.Nativida，博士论文，菲律宾大学Diliman，菲律宾，2004]所使用的方法，并对Ling和Solé[S.Ling，P.Solé，关于准循环码的代数结构I：有限域，IEEE翻译》开发的一类准循环码的代数结构使用了广义离散傅立叶变换。通知我。理论47(2001)2751-2760]。
Ling and Solé [S. Ling, P. Solé, On the algebraic structure of quasi-cyclic codes I: Finite fields, IEEE Trans. Inform. Theory 47 (2001) 2751–2760] showed that every quasi-cyclic code C is constructed from shorter linear codes which are called the constituent codes of C. Given a quasi-cyclic code C of length ℓm and index ℓ with m being pairwise coprime to ℓ and the order of the field C is over, if all its constituent codes are cyclic with their zeroes having full multiplicity, C is then shown to be equivalent to a cyclic code whose zeroes with their multiplicities are fully described in terms of the nonzeroes of the cyclic constituent codes. The general transformation to obtain the above-mentioned equivalent cyclic code is also explicitly given. The approach adopted here follows the approach used by A.M.A. Natividad [A.M.A. Natividad, PhD thesis, Department of Mathematics, University of Philippines Diliman, The Philippines, 2004] and uses the generalized discrete Fourier transform on the algebraic structure of the class of quasi-cyclic codes developed by Ling and Solé [S. Ling, P. Solé, On the algebraic structure of quasi-cyclic codes I: Finite fields, IEEE Trans. Inform. Theory 47 (2001) 2751–2760].