• 제목/요약/키워드: complete weight enumerators

검색결과 4건 처리시간 0.019초

WEIGHT ENUMERATORS OF TWO CLASSES OF LINEAR CODES

  • Ahn, Jaehyun;Ka, Yeonseok
    • 충청수학회지
    • /
    • 제33권1호
    • /
    • pp.43-56
    • /
    • 2020
  • Recently, linear codes constructed from defining sets have been studied widely and determined their complete weight enumerators and weight enumerators. In this paper, we obtain complete weight enumerators of linear codes and weight enumerators of linear codes. These codes have at most three weight linear codes. As application, we show that these codes can be used in secret sharing schemes and authentication codes.

MACWILLIAMS IDENTITIES OVER $M_n\times_s(Z_4)$ WITH RESPECT TO THE RT METRIC

  • Zhu, Shi-Xin;Xu, He-Qian
    • Journal of applied mathematics & informatics
    • /
    • 제26권1_2호
    • /
    • pp.107-120
    • /
    • 2008
  • There has been a recent growth of interest in codes with respect to a newly defined non-Hamming metric grown as the Rosenbloom-Tsfasman metric (RT, or $\rho$, in short). In this paper, the definitions of the Lee complete $\rho$ weight enumerator and the exact complete $\rho$ weight enumerator of a code over $M_n_\times_s(Z_4)$ are given, and the MacWilliams identities with respect to this RT metric for the two weight enumerators of a linear code over $M_n_\times_s(Z_4)$ are proven too. At last, we also prove that the MacWilliams identities for the Lee and exact complete $\rho$ weight enumerators of a linear code over $M_n_\times_s(Z_4)$ are the generalizations of the MacWilliams identities for the Lee and complete weight enumerators of the corresponding code over $Z_4$.

  • PDF

ON ℤpp[u]/k>-CYCLIC CODES AND THEIR WEIGHT ENUMERATORS

  • Bhaintwal, Maheshanand;Biswas, Soumak
    • 대한수학회지
    • /
    • 제58권3호
    • /
    • pp.571-595
    • /
    • 2021
  • In this paper we study the algebraic structure of ℤpp[u]/k>-cyclic codes, where uk = 0 and p is a prime. A ℤpp[u]/k>-linear code of length (r + s) is an Rk-submodule of ℤrp × Rsk with respect to a suitable scalar multiplication, where Rk = ℤp[u]/k>. Such a code can also be viewed as an Rk-submodule of ℤp[x]/r - 1> × Rk[x]/s - 1>. A new Gray map has been defined on ℤp[u]/k>. We have considered two cases for studying the algebraic structure of ℤpp[u]/k>-cyclic codes, and determined the generator polynomials and minimal spanning sets of these codes in both the cases. In the first case, we have considered (r, p) = 1 and (s, p) ≠ 1, and in the second case we consider (r, p) = 1 and (s, p) = 1. We have established the MacWilliams identity for complete weight enumerators of ℤpp[u]/k>-linear codes. Examples have been given to construct ℤpp[u]/k>-cyclic codes, through which we get codes over ℤp using the Gray map. Some optimal p-ary codes have been obtained in this way. An example has also been given to illustrate the use of MacWilliams identity.