Title: On the structure and distances of repeated-root constacyclic codes
Speaker: Anuradha Sharma (IIIT, Delhi)
Date: 03 December 2018
Time: 3 pm
Venue: LH-1, Mathematics Department
The main aim of coding theory is to construct codes that are easier to encode
and decode, can correct or at least detect many errors, and contain a
sufficiently large number of codewords. To study error-detecting and
error-correcting properties of a code with respect to various communication
channels, several metrics (e.g. Hamming metric, Lee metric, Rosenbloom-Tsfasman
(RT) metric, symbol-pair metric, etc.) have been introduced and studied in
In this talk, we will establish algebraic structures of all repeated-root
constacyclic codes of prime power lengths over finite commutative chain rings.
Using their algebraic structures, we will determine Hamming distances,
b-symbol distances, RT distances, and RT weight distributions of these codes.
As an application of these results, we will identify MDS (maximum-distance
separable) Hamming, MDS b-symbol and MDS RT codes within this particular
class of constacyclic codes. We will also present an algorithm to decode
these codes with respect to the Hamming, symbol-pair and RT metrics.