BiD Codes: Algebraic Codes from 3 × 3 Kernel
Abstract
We introduce Berman-intersection-dual Berman (BiD) codes. These are abelian codes of length 3m that can be constructed using Kronecker products of a 3 × 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 35=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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