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Designs, Codes and Cryptography

, Volume 52, Issue 2, pp 171–183 | Cite as

A new extension theorem for 3-weight modulo q linear codes over \({\mathbb{F}_q}\)

  • E. J. Cheon
  • T. Maruta
Article

Abstract

We prove that every [n, k, d] q code with q ≥ 4, k ≥ 3, whose weights are congruent to 0, −1 or −2 modulo q and \({d \equiv -1 \pmod{q}}\) is extendable unless its diversity is \({\left({q \choose 2}q^{k-3}+\theta_{k-3}, {q\choose 2}q^{k-3}\right)}\) for odd q, where \({\theta_j = (q^{j+1}-1)/(q-1)}\) .

Keywords

Extension theorem Linear code 3-weight Projective space 

Mathematics Subject Classification (2000)

94B65 94B05 51E20 05B25 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of Mathematics and RINSGyeongsang National UniversityJinjuKorea
  2. 2.Department of Mathematics and Information SciencesOsaka Prefecture UniversitySakai, OsakaJapan

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