대한수학회지 (Journal of the Korean Mathematical Society)

  • 제44권5호
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  • Pages.1139-1162
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  • 2007
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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OPTIMAL LINEAR CODES OVER ℤm

  • 발행 : 2007.09.30
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초록

We examine the main linear coding theory problem and study the structure of optimal linear codes over the ring ${\mathbb{Z}}_m$. We derive bounds on the maximum Hamming weight of these codes. We give bounds on the best linear codes over ${\mathbb{Z}}_8$ and ${\mathbb{Z}}_9$ of lengths up to 6. We determine the minimum distances of optimal linear codes over ${\mathbb{Z}}_4$ for lengths up to 7. Some examples of optimal codes are given.

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참고문헌

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피인용 문헌

  1. MDS and self-dual codes over rings vol.18, pp.6, 2012, https://doi.org/10.1016/j.ffa.2012.09.003
  2. The number of self-dual codes over $${Z_{p^3}}$$ vol.50, pp.3, 2009, https://doi.org/10.1007/s10623-008-9232-4
  3. MDS codes over finite principal ideal rings vol.50, pp.1, 2009, https://doi.org/10.1007/s10623-008-9215-5
  4. The classification of self-dual modular codes vol.17, pp.5, 2011, https://doi.org/10.1016/j.ffa.2011.02.010