HOẠT ĐỘNG TRONG TUẦN

Constacyclic codes with finite chain ring alphabets: algebraic structures, distances, and applications
Báo cáo viên: Đinh Quang Hải (Kent State Univ.)

Thời gian: 9h, Thứ 4 ngày 7 tháng 8 năm 2019

Địa điểm: Phòng 507, tầng 5 nhà A6 Viện Toán

Tóm tắt: Unlike the simple-root case, it is shown that the ambient rings of repeated-root constacyclic codes over finite chain rings are usually not principal ideal rings. We discuss the algebraic structure of repeated-root $lambda$-constacyclic codes of prime power length $p^s$ over any finite commutative chain ring $R$. It is proven that the ambient ring $frac{R[x]}{langle x^{p^s}-lambda rangle}$ is a local ring with maximal ideal $langle x-lambda, gamma rangle$. Among other things, the nilpotency indices of $x-1$ and $x+1$ in the ambient rings $frac{R[x]}{langle x^{p^s}-1 rangle}$ and $frac{R[x]}{langle x^{p^s}+1 rangle}$, respectively, are established. We will also discuss some special cases of the chain ring $R$ that were studied in the literature, as well as some generalizations on the lengths and alphabets of the codes.

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