대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제60권5호
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  • Pages.1237-1252
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  • 2023
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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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)
  • 투고 : 2022.09.05
  • 심사 : 2023.04.21
  • 발행 : 2023.09.30
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초록

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.

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과제정보

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

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