The Journal of Korean Institute of Communications and Information Sciences (한국통신학회논문지)

The Korean Institute of Commucations and Information Sciences (한국통신학회)
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New Proof of Minimum Distance for Binary Cyclic Codes with $d_{min}$=5

최소거리가 5인 이진 순회부호의 최소거리에 관한 새로운 증명

  • Published : 2000.10.01
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Abstract

We investigated into the minimum distance of a primitive binary cyclic code C with a generator polynomial g(x)=$m_1(x)m_{d}(x)$. It is known that the necessary and sufficient condition for C to have minimum distance five is the fact that \ulcorner is an APN power function. In this paper we derived the new proof of minimum distance for the primitive binary cyclic codes with minimum distance five.

부호길이가 $2^{n}-1$이고 생성다항식이 g(x)=$m_1(x)m_{d}(x)$인 이진 순회부호에서 최소거리가 5가 되기 위한 조건은 $x^{d}$가 APN 함수라는 것으로 이는 이미 알려진 내용인데 이에 관한 새로운 증명을 제시하였다.

Keywords

References

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