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In this paper, we consider the structure of $\gamma$-constacyclic codes of length $2p^s$ over the Galois ring ${\rm GR}(p^a,m)$ for any unit $\gamma$ of the form $\xi_0+p\xi_1+p^2z$, where $z\in {\rm GR}(p^a,m)$ and $\xi_0, \xi_1$ are nonzero elements of the set $\mathcal{T}(p,m)$. Here $\mathcal{T}(p,m)$ denotes a complete set of representatives of the cosets $\frac{{\rm GR}(p^a,m)}{p{\rm GR}(p^a,m)} = \mathbb{F}_{p^m}$ in ${\rm GR}(p^a,m)$. When $\gamma$ is not a square, the rings $\mathcal{R}_{p}(a,m,\gamma)=\frac{{\rm GR}(p^a,m)[x]}{\langle x^{2p^s}-\gamma\rangle}$ is a chain ring with maximal ideal $\langle x^2-\delta\rangle$, where $\delta^{p^s}=\xi_0$, and the number of codewords of $\gamma$-constacyclic code are provided. Furthermore, the self-orthogonal and self-dual $\gamma$-constacyclic codes of length $2p^s$ over ${\rm GR}(p^a,m)$ are also established. Finally, we determine the Rosenbloom-Tsfasman (RT) distances and weight distributions of all such codes.
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참고문헌 (28)
참고문헌 신청
T. Abualrub / 2003 / On the generators of Z4 cyclic codes of length 2e / IEEE Trans. Inform. Theory 49(9):2126~2133
E. R. Berlekamp / 1969 / Negacyclic codes for the Lee metric / Combinatorial Mathematics and its Applications (Proc. Conf., Univ. North Carolina, Chapel Hill, N.C., 1967) :298~316
S. D. Berman / 1967 / Semisimple cyclic and Abelian codes. II / Cybernetics 3(3):17~23
T. Blackford / 2003 / Negacyclic codes over Z4 of even length / IEEE Trans. Inform. Theory 49(6):1417~1424
A. R. Calderbank / 1993 / A linear construction for certain Kerdock and Preparata codes / Bull. Amer. Math. Soc. 29(2):218~222
E. R. Berlekamp / 1969 / Negacyclic codes for the Lee metric / Combinatorial Mathematics and its Applications (Proc. Conf., Univ. North Carolina, Chapel Hill, N.C., 1967) :298~316
S. D. Berman / 1967 / Semisimple cyclic and Abelian codes. II / Cybernetics 3(3):17~23
T. Blackford / 2003 / Negacyclic codes over Z4 of even length / IEEE Trans. Inform. Theory 49(6):1417~1424
A. R. Calderbank / 1993 / A linear construction for certain Kerdock and Preparata codes / Bull. Amer. Math. Soc. 29(2):218~222
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