BiD Codes: Algebraic Codes from $3 \times 3$ Kernel
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908448798539776 |
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| author | Dash, Anirudh Nandakishore, K. R. Natarajan, Lakshmi Prasad Krishnan, Prasad |
| author_facet | Dash, Anirudh Nandakishore, K. R. Natarajan, Lakshmi Prasad Krishnan, Prasad |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10068 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | BiD Codes: Algebraic Codes from $3 \times 3$ Kernel Dash, Anirudh Nandakishore, K. R. Natarajan, Lakshmi Prasad Krishnan, Prasad Information Theory 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. |
| title | BiD Codes: Algebraic Codes from $3 \times 3$ Kernel |
| topic | Information Theory |
| url | https://arxiv.org/abs/2507.10068 |