Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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OPTIMAL LINEAR CODES OVER ℤm

  • Published : 2007.09.30
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Abstract

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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References

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