Noncyclic BCH and Srivastava codes over Eisenstein integers toward next-generation error-correcting codes

This article investigates noncyclic BCH and Srivastava codes over Eisenstein integer fields ${\mathbb{Z}}_p[\omega ]$, where $p\equiv 2(\mathrm{mod}3)$. By leveraging the algebraic structure of Eisenstein fields, we construct parity-check matrices with an alternant structure such that all maximal-order determinants satisfy the required algebraic conditions. These constructions provide explicit lower bounds on the minimum distance and enhance the error-correcting performance of the codes. The study further generalizes noncyclic forms of BCH and Srivastava codes, enabling higher code rates and larger minimum distances than their cyclic counterparts. Numerical examples illustrate the feasibility and effectiveness of the proposed constructions for reliable data transmission.