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Applicable Algebra in Engineering, Communication and Computing
Published in: Applicable Algebra in Engineering, Communication and Computing 6/2017

18-04-2017 | Original Paper

An improved method for determining the weight distribution of a family of q-ary cyclic codes

Author: Gerardo Vega

Published in: Applicable Algebra in Engineering, Communication and Computing | Issue 6/2017

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Abstract

The purpose of this work is to use an already known identity among the weight enumerator polynomials, in order to present an improved method for determining the weight distribution of a family of q-ary reducible cyclic codes, that generalize, in an easier way, the results in Yu and Liu (Des Codes Cryptogr 78:731–745, 2016).
previous article Spaces of directed paths on pre-cubical sets
next article Linear codes from quadratic forms

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Literature
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Helleseth, T., Kholosha, A.: Monomial and quadratic bent functions over the finite fields of odd characteristic. IEEE Trans. Inf. Theory 52(5), 2018–2032 (2006)CrossRefMATHMathSciNet
2.
Helleseth, T., Kløve, T., Mykkeltveit, J.: The weight distribution of irreducible cyclic codes with block lengths \(n_1((q^l-1)N)\). Discrete Math. 18(2), 179–211 (1977)CrossRefMATHMathSciNet
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MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error-Correcting Codes. North-Holland, Amsterdam (1977)MATH
5.
Vega, G.: Determining the number of one-weight cyclic codes when length and dimension are given. Lect. Notes Comput. Sci. 4547, 284–293 (2007)CrossRefMATHMathSciNet
6.
Vega, G.: A critical review and some remarks about one- and two-weight irreducible cyclic codes. Finite Fields Their Appl. 51(33), 1–13 (2015)CrossRefMATHMathSciNet
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Metadata
Title
An improved method for determining the weight distribution of a family of q-ary cyclic codes
Author
Gerardo Vega
Publication date
18-04-2017
Publisher
Springer Berlin Heidelberg
Published in
Applicable Algebra in Engineering, Communication and Computing / Issue 6/2017
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI
https://doi.org/10.1007/s00200-017-0318-y

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