Symbol-Pair and Symbol-Triple Distances of Repeated-Root Constacylic Codes of Prime Power Lengths over Finite Fields
Báo cáo viên: Dinh Hai (USA)

Thời gian: 9h, Thứ 4, ngày 8 tháng 1 năm 2020

Địa điểm: Phòng 611-612, Nhà A6, Viện Toán học

Tóm tắt: Let $p$ be an odd prime, $s$ and $m$ be positive integers and $lambda$ be a nonzero element of the finite field $mathbb{F}_{p^m}$. The $lambda$-constacyclic codes of length $p^s$ over $mathbb{F}_{p^m}$ are linearly ordered under set theoretic inclusion as ideals of the chain ring $mathbb{F}_{p^m}[x]/langle x^{p^s}-lambda rangle$. Using this structure, the symbol-pair and symbol-triple distances of all such $lambda-$constacyclic codes are established in this talk. All maximum distance separable symbol-pair and symbol-triple constacyclic codes of length $p^s$ are also determined as an application. We will discuss possible generalizations of these concepts to the most general case of multy-symbol constacylic codes and longer code lengths.

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