Several new classes of linear codes with few weights

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Abstract

Let \(\phantom {\dot {i}\!}\mathbb {F}_{q}\) be a finite field of order q, where q = p s is a power of a prime number p. Let m and m1 be two positive integers such that m1 divides m. For any positive divisor e of q − 1, we construct an infinite family of codes with dimension m + m1 and few weights over \(\phantom {\dot {i}\!}\mathbb {F}_{q}\). Using Gauss sum, their weight distributions are provided. When gcd(e, m) = 1, we obtain a subclass of optimal codes which attain the Griesmer bound. Moreover, when gcd(e, m) = 2 or 3 we construct new infinite families of codes with at most four weights.

Keywords

Linear codes Weight distribution Gauss sum 

Mathematics Subject Classification 2010

94B05 94B15 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsCentral China Normal UniversityWuhanChina
  2. 2.Department of MathematicsUniversity of Sciences and Technology HOUARI BOUMEDIENEAlgerAlgeria

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