Poset weight enumerators
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Jurrius et al. give the explicit identities for relations among various weight enumerators with respect to Hamming weight [4]. These identities show the connections between coding theory and graph theory. In this paper, we generalize the weight enumerators of a code with respect to poset weight: (i) poset weight enumerator, (ii) r-th higher poset weight enumerator, (iii) extension poset weight enumerator and (iv) poset Tutte polynomial. And we give the relations among these enumerators that are the connection between poset codes and graph theory.
Abstract
Jurrius et al. give the explicit identities for relations among various weight enumerators with respect to Hamming weight [4]. These identities show the connections between coding theory and graph theory. In this paper, we generalize the weight enumerators of a code with respect to poset weight: (i) poset weight enumerator, (ii) r-th higher poset weight enumerator, (iii) extension poset weight enumerator and (iv) poset Tutte polynomial. And we give the relations among these enumerators that are the connection between poset codes and graph theory.
참고문헌 (7)
- Richard A. Brualdi, "Codes with a poset metric", Discrete Math., 147(1-3), pp.57~72 (1995)
- Curtis Greene, "Weight enumeration and the geometry of linear codes", Studies in Applied Math-ematics, 55(2), pp.119~128 (1976)
- W.C. Hufiman, "Fundamentals of Error-Correcting Codes" (2010), Cambridge University Press
- R. Jurrius, "Extended and generalized weight enumerators", Proceedings of the International Workshop on Coding and Cryptography(WCC) (2009)
- 김동찬, "Several weight enumerators and zeta polynomials of linear codes", 박사, 수학과, pp.2013
- F. J. MacWilliams, "The Theory of Error-Correcting Codes" (1988), North Holland Publishing Co.
- D. J. A. Welsh, "Matroid theory" (1976), Academic Press