About the nth-Root Codes: a Gröbner Basis Approach to the Weight Computation

Marta Giorgetti ()
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Marta Giorgetti: University of Milano, Department of Mathematics

A chapter in Gröbner Bases, Coding, and Cryptography, 2009, pp 357-360 from Springer

Abstract: Abstract Recently some methods have been proposed to find the distance and weight distribution of cyclic codes using Gröbner bases (Sala in Appl. Algebra Engrg. Comm. Comput. 13(2):137–162, 2002; Mora and Sala in J. Symbolic Comput. 35(2):177–194, 2003). We identify a class of codes for which these methods can be generalized. We show that this class contains all interesting linear codes (i.e., with d≥2) and we provide variants and improvements.

Keywords: Natural Number; Weight Distribution; Basis Approach; Linear Code; Discrete Mathematic (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-93806-4_20

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DOI: 10.1007/978-3-540-93806-4_20

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