{
  "annotation_id": "dfa2a9de-a37b-463d-bc48-10d599080173",
  "date_created": "2026-02-17T05:53:19.909000Z",
  "date_modified": "2026-02-17T05:53:19.909000Z",
  "file_hash": "c4e5a54f27921bd011bfa4216dcd5a31da7175d486eb7d4046d4905f45b56193",
  "private": false,
  "record": {
    "abstract": "BiD codes, which are a new family of algebraic codes of length $3^m$, achieve the erasure channel capacity under bit-MAP decoding and offer asymptotically larger minimum distance than Reed-Muller (RM) codes. In this paper we propose fast maximum-likelihood (ML) and max-log-MAP decoders for first-order BiD codes. For second-order codes, we identify their minimum-weight parity checks and ascertain a code property known as \u0027projection\u0027 in the RM coding literature. We use these results to design a belief propagation decoder that performs within 1 dB of ML decoder for block lengths 81 and 243.",
    "arxiv_id": "2601.09390",
    "authors": [
      "Devansh Jain",
      "Lakshmi Prasad Natarajan"
    ],
    "categories": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "On Decoding First- and Second-Order BiD Codes",
    "url": "https://arxiv.org/abs/2601.09390",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "fd5c896f-1b1a-4010-90de-295edf8e206d",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}