一类最小距离超过BCH界的循环码

2012 XIII International Symposium on Problems of Redundancy in Information and Control Systems Pub Date : 2012-10-25 DOI:10.1109/RED.2012.6338404

V. Lomakov

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引用次数: 3

摘要

证明了在有限域GF(p)上，对于任意素数p和任意整数r≥1，存在一个长度为p (r +1) - 1，维数为p (r +1) - 1(p +1 - 2)的循环码，其最小距离≥p + 2 r大于或等于BCH界p + 2。

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On a class of cyclic codes whose minimum distance exceeds the BCH bound

It is shown that for any prime p and any integer ℓ ≥ 1, there is a cyclic code of length p^2(ℓ+1) - 1 and dimension p^ℓ+1(p^ℓ+1 - 2) over the finite field GF(p) whose minimum distance ≥ p + 2ℓ is greater than or equal to the BCH bound p + 2.

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2012 XIII International Symposium on Problems of Redundancy in Information and Control Systems

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