On Classical and Quantum MDS-Convolutional BCH Codes

TL;DR

This paper introduces new algebraic constructions of classical and quantum convolutional BCH codes with multi-memory and unit-memory, achieving optimality by meeting the generalized Singleton bound, without relying on computational search.

Contribution

It presents algebraic methods to construct optimal classical and quantum convolutional BCH codes with multi-memory and unit-memory, expanding the coding theory landscape.

Findings

Constructed new families of multi-memory classical convolutional BCH codes.

Developed families of unit-memory quantum convolutional codes.

Codes attain the classical and quantum generalized Singleton bound.

Abstract

Several new families of multi-memory classical convolutional Bose-Chaudhuri-Hocquenghem (BCH) codes as well as families of unit-memory quantum convolutional codes are constructed in this paper. Our unit-memory classical and quantum convolutional codes are optimal in the sense that they attain the classical (quantum) generalized Singleton bound. The constructions presented in this paper are performed algebraically and not by computational search.