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1-generator quasi-cyclic codes. (English) Zbl 1169.94346

Summary: This paper discusses the enumeration of 1-generator quasi-cyclic codes and describes an algorithm which will obtain one, and only one, generator for each 1-generator quasi-cyclic code.

MSC:

94B15 Cyclic codes
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References:

[1] G. E. Séguin, A class of 1-generator quasi-cyclic codes, IEEE Trans. Inform. Theory, 2004, 50: 1745–1753. · Zbl 1298.94138 · doi:10.1109/TIT.2004.831861
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[7] S. Ling and P. Solé, On the algebraic structure quasi-cyclic codes II: chain rings, Designs, Codes, and Crypotography, 2003, 30: 113–130. · Zbl 1032.94011 · doi:10.1023/A:1024715527805
[8] B. K. Dey and B. S. Rajan, \({\mathbb{F}}_q\) -linear cyclic codes over \({\mathbb{F}}_{q^m}\) : DFT characterization, in Lecture Notes in Computer Science (ed. by S. Bozatas and I. E. Shparlinski), 2001, 2227: 67–76. · Zbl 1057.94025
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