The Journal of the Korea institute of electronic communication sciences (한국전자통신학회논문지)

Korea Institute of Electronic Communication Science (한국전자통신학회)
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MWCA Test using 90/150 HCA

90/150 HCA를 이용한 MWCA 판정법

  • 최언숙 (동명대학교 정보통신공학과) ;
  • 조성진 (부경대학교 응용수학과) ;
  • 김한두 (인제대학교 컴퓨터공학부) ;
  • 김진경 (부경대학교 응용수학과) ;
  • 강성원 (부경대학교 응용수학과)
  • Received : 2018.12.04
  • Accepted : 2019.02.15
  • Published : 2019.02.28
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Abstract

Self-reciprocal polynomials over finite fields are useful in several applications, including reversible codes with read-backward properties. This paper is a study on 90/150 CA with characteristic polynomials of maximal weight polynomials, which is one of the self-reciprocal polynomials. In this paper, we propose a decision method for determining the existence of 90/150 MWCA corresponding to the maximum weight polynomial of degree 2n using n-cell 90/150 CA with transition rule <$100{\cdots}0$>. The proposed method is verified through experiments.

유한체 상에서 자기상반다항식은 역방향읽기 성질을 갖는 가역 부호를 설계하는 데 유용하다. 본 논문은 자기상반다항식 중 하나인 최대무게 다항식을 특성다항식으로 갖는 90/150 CA에 관한 연구이다. 전이규칙이 <$100{\cdots}0$>인 n-셀 90/150 CA를 이용하여 2n차 최대무게 다항식에 대응하는 90/150 MWCA가 존재하는지에 대한 판정법을 제안한다. 제안하는 방법은 실험을 통하여 검증한다.

Keywords

KCTSAD_2019_v14n1_235_f0001.png 이미지

그림 1. 전이규칙 <0001>인 90/150 CA의 구조 Fig. 1 Structure of 90/150 CA with transition rule <0001>

표 1. 전이규칙 90과 150의 부울식 Table 1. Boolean equation for transition rule 90 and 150

KCTSAD_2019_v14n1_235_t0001.png 이미지

표 2. f1(x)부터 f200(x)까지 90/150 MWCA가 존재하지 않는 차수 Table 2. The degree of the polynomials for which there is no 90/150 MWCA from f1(x) to f200(x)

KCTSAD_2019_v14n1_235_t0002.png 이미지

표 3. 90/150 MWCA 판정 알고리즘 Table 3. 90/150 MWCA decision algorithm

KCTSAD_2019_v14n1_235_t0003.png 이미지

표 4. 90/150 MWCA 판정 알고리즘을 이용한 hm(x)의 인수분해와 f2m(x)의 판정 결과 Table 4. Results of f2m(x) and factorization of hm(x) using 90/150 MWCA decision algorithm

KCTSAD_2019_v14n1_235_t0004.png 이미지

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