BiD Codes: Algebraic Codes from $3 \times 3$ Kernel
Information Theory
2025-07-15 v1 math.IT
Abstract
We introduce Berman-intersection-dual Berman (BiD) codes. These are abelian codes of length that can be constructed using Kronecker products of a kernel matrix. BiD codes offer minimum distance close to that of Reed-Muller (RM) codes at practical blocklengths, and larger distance than RM codes asymptotically in the blocklength. Simulations of BiD codes of length in the erasure and Gaussian channels show that their block error rates under maximum-likelihood decoding are similar to, and sometimes better, than RM, RM-Polar, and CRC-aided Polar codes.
Cite
@article{arxiv.2507.10068,
title = {BiD Codes: Algebraic Codes from $3 \times 3$ Kernel},
author = {Anirudh Dash and K. R. Nandakishore and Lakshmi Prasad Natarajan and Prasad Krishnan},
journal= {arXiv preprint arXiv:2507.10068},
year = {2025}
}
Comments
Accepted for presentation and publication at the 2025 IEEE Information Theory Workshop (ITW'25)