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

Time: 9h00, Wednesday, January 8, 2020,
Room 611-612, Building A6, Institute of Mathematics
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.