Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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NONEXISTENCE OF SOME EXTREMAL SELF-DUAL CODES

  • Han, Sun-Ghyu (Mathematics Section College of Science Yonsei University) ;
  • Lee, June-Bok (Mathematics Section College of Science Yonsei University)
  • Published : 2006.11.01
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Abstract

It is known that if C is an [24m + 2l, 12m + l, d] selfdual binary linear code with $0{\leq}l<11,\;then\;d{\leq}4m+4$. We present a sufficient condition for the nonexistence of extremal selfdual binary linear codes with d=4m+4,l=1,2,3,5. From the sufficient condition, we calculate m's which correspond to the nonexistence of some extremal self-dual binary linear codes. In particular, we prove that there are infinitely many such m's. We also give similar results for additive self-dual codes over GF(4) of length n=6m+1.

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References

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  5. Singly even self-dual codes of length 24k + 10 and minimum weight 4k + 2 pp.1936-2455, 2018, https://doi.org/10.1007/s12095-018-0303-8