On quasi-cyclic codes over $${\mathbb{Z}_q}$$
On quasi-cyclic codes over $${\mathbb{Z}_q}$$
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DOI：
10.1007/s00200-009-0110-8
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发表时间：
2009-11
期刊：
影响因子：
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通讯作者：
Maheshanand Bhaintwal;S. Wasan
中科院分区：
文献类型：
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作者：
Maheshanand Bhaintwal;S. Wasan
准循环（QC）码是循环码的显着推广。许多 QC 代码已被证明最适合其参数。本文考虑了质数幂整数余数环上QC码的一些结构性质。 lengthlover 的 Anl-QC 代码既被视为传统的行循环形式，也被视为 的子模，其中 GR(q,l) 是 Degreelover 的伽罗瓦扩展环。给出了伽罗瓦环上的循环码自由的充要条件，并给出了它们的BCH类型。给出了1-生成器QC码自由的充分条件，并推导了评估其等级的公式。还讨论了 1 生成器 QC 代码的一些距离界限。还简要讨论了 QC 代码的对偶。
Quasi-cyclic (QC) codes are a remarkable generalization of cyclic codes. Many QC codes have been shown to be best for their parameters. In this paper, some structural properties of QC codes over the prime power integer residue ringare considered. Anl-QC code of lengthlmoveris viewed both as in the conventional row circulant form and also as a-submodule of, whereGR(q,l) is the Galois extension ring of degreelover. A necessary and sufficient condition for cyclic codes over Galois rings to be free is obtained and a BCH type bound for them is also given. A sufficient condition for 1-generator QC codes to be-free is given and a formula to evaluate their ranks is derived. Some distance bounds for 1-generator QC codes are also discussed. The duals of QC codes overare also briefly discussed.