Journal of the Korea Institute of Information Security & Cryptology (정보보호학회논문지)

Korea Institute of Information Security and Cryptology (한국정보보호학회)
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New Cyclic Relative Difference Sets Constructed from d-Homogeneous Functions with Difference-balanced Property

차균형성질을 갖는 d-동차함수로부터 생성된 새로운 순회상대차집합

  • 김상효 (서울대학교 전기·컴퓨터공학부) ;
  • 노종선 (서울대학교 전기·컴퓨터공학부)
  • Published : 2002.04.01
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Abstract

In this paper, for many prime power q, it is shown that new cyclic relative difference sets with parameters (equation omitted) can be constructed by using d-homogeneous functions on $F_{q^{n}}${0} over $F_{q}$ with difference-balanced property, where $F_{q^{n} }$ is a finite field with $q^{n}$ elements. Several new cyclic relative difference sets with parameters (equation omitted) are constructed by using p-ary sequences of period $q^{n}$ -1 with ideal autocorrelation property introduced by Helleseth and Gong and d-form sequences.

본 논문에서는 q는 p의 멱승이고, $F_{q^{n}}$이 원소의 개수가 $q^{n}$ 개인 유한체라 할 때, $F_{q^{n}}${0}으로부터의 $F_{q}$ 로의 차균형 성질을 갖는 d-동차함수로부터 (equation omitted) 순회상대차집합이 얻어질 수 있음을 보인다. 이에 따라 주기가 $q^{n}$ -1이고, 이상적인 자기상관성질을 갖는 p진 시퀀스 Helleseth-Gong 시퀀스 및, d-형 시퀀스로부터 (equation omitted)의 파라미터를 갖는 새로운 순회상대차집합을 생성시킨다.

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References

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