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arXiv · 2507.10068

BiD Codes: Algebraic Codes from $3 \times 3$ Kernel

Anirudh Dash·K. R. Nandakishore·Lakshmi Prasad Natarajan·Prasad Krishnan
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Abstract

We introduce Berman-intersection-dual Berman (BiD) codes. These are abelian codes of length $3^m$ that can be constructed using Kronecker products of a $3 \times 3$ 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 $3^5=243$ 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.

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Anirudh Dash, K. R. Nandakishore, Lakshmi Prasad Natarajan, Prasad Krishnan. 2025-07-14. BiD Codes: Algebraic Codes from $3 \times 3$ Kernel. https://arxiv.org/abs/2507.10068

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