Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON THE CONSTRUCTION OF OPTIMAL LINEAR CODES OF DIMENSION FOUR

  • Atsuya Kato (Department of Mathematical Sciences Osaka Prefecture University) ;
  • Tatsuya Maruta (Department of Mathematics Osaka Metropolitan University) ;
  • Keita Nomura (Department of Mathematical Sciences Osaka Prefecture University)
  • Received : 2022.09.05
  • Accepted : 2023.04.21
  • Published : 2023.09.30
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Abstract

A fundamental problem in coding theory is to find nq(k, d), the minimum length n for which an [n, k, d]q code exists. We show that some q-divisible optimal linear codes of dimension 4 over 𝔽q, which are not of Belov type, can be constructed geometrically using hyperbolic quadrics in PG(3, q). We also construct some new linear codes over 𝔽q with q = 7, 8, which determine n7(4, d) for 31 values of d and n8(4, d) for 40 values of d.

Keywords

Acknowledgement

The authors want to express their gratitude to the referee for the helpful comments and suggestions.

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