Pith Number

pith:WNKYIIFW

pith:2026:WNKYIIFWOVJBPWA5RTML73LTU5

not attested not anchored not stored refs pending

Linear and cyclic codes over some special rings

Bianca Liana Bercea-Straton, Cristina Flaut

Linear and cyclic codes are defined over the ring Z2[u,v] modulo u squared times (1 plus u) and v squared times (1 plus v squared).

arxiv:2605.03031 v2 · 2026-05-04 · cs.IT · math.IT · math.RA

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\usepackage{pith}
\pithnumber{WNKYIIFWOVJBPWA5RTML73LTU5}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

In this paper, we describe linear and cyclic codes over the ring Z2[u,v](u2(1+u),v2(1+v2)).

C2weakest assumption

The given ring admits the standard definitions of linear and cyclic codes without additional compatibility conditions that would invalidate the usual generator-matrix or ideal-based constructions.

C3one line summary

Linear and cyclic codes are described over the ring Z₂[u,v]/(u²(1+u), v²(1+v²)).

Receipt and verification

First computed	2026-05-28T02:04:48.888014Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b3558420b6755217d81d8cd8bfed73a75679645b4200824077b14242afe073ca

Aliases

arxiv: 2605.03031 · arxiv_version: 2605.03031v2 · doi: 10.48550/arxiv.2605.03031 · pith_short_12: WNKYIIFWOVJB · pith_short_16: WNKYIIFWOVJBPWA5 · pith_short_8: WNKYIIFW

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/WNKYIIFWOVJBPWA5RTML73LTU5 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: b3558420b6755217d81d8cd8bfed73a75679645b4200824077b14242afe073ca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6e3e40c92ff681653d87795193f475b8109a5084686768b5cf4a8b12bbefcadb",
    "cross_cats_sorted": [
      "math.IT",
      "math.RA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-05-04T18:02:03Z",
    "title_canon_sha256": "17417fd27ddeb4ec1d1fa851f9383c3ee04fbbe176ce971eea60b28683ec5976"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.03031",
    "kind": "arxiv",
    "version": 2
  }
}