Pith Number

pith:V4NHCTIZ

pith:2026:V4NHCTIZ7I2NKIH6A2EIKFCZGI

not attested not anchored not stored refs resolved

Intermediate Constacyclic Codes and Scalar-Residue Reed--Muller Layers

Yaoran Yang, Yutong Zhang

The minimum distance of intermediate constacyclic codes equals an explicit case formula in the field size q and the parameters a and b of the degree ℓ.

arxiv:2605.17022 v1 · 2026-05-16 · cs.IT · math.IT

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Claims

C1strongest claim

If ℓ=(q-1)a+b<(q-1)m-1, 0≤b≤q-2, and b≡r-1 (mod r), then for every prime power q, every divisor r of q-1 with 2<r<q-1, and every m≥2, d(C(q,m,r,ℓ)) equals (q-1)/r *(q-b+1)q^{m-a-2} when 0≤a≤m-2 and (q-b+r-2)/r when a=m-1.

C2weakest assumption

The proof relies on the hidden scalar homogeneity of the evaluation model for these codes, which is invoked to enable the orbit-counting obstruction and the homogeneous pencil construction that attain the claimed distances and supports.

C3one line summary

Proves that the minimum distance of intermediate constacyclic codes C(q,m,r,ℓ) equals a specific piecewise formula and determines the minimum affine support for non-terminal scalar-residue layers of generalized Reed-Muller codes.

References

19 extracted · 19 resolved · 0 Pith anchors

[1] Two classes of constacyclic codes with variable parameters[(q m −1)/r, k, d], 2024

[2] Two classes of constacyclic codes with a square-root-like lower bound, 2024

[3] On generalized Reed–Muller codes and their relatives, 1970

[4] On the weight enumeration of weights less than2.5dof Reed–Muller codes, 1976

[5] On the weight structure of Reed–Muller codes, 1970

Receipt and verification

First computed	2026-05-20T00:03:36.414087Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

af1a714d19fa34d520fe068885145932223275303a479f29a6569add3d10a8c4

Aliases

arxiv: 2605.17022 · arxiv_version: 2605.17022v1 · doi: 10.48550/arxiv.2605.17022 · pith_short_12: V4NHCTIZ7I2N · pith_short_16: V4NHCTIZ7I2NKIH6 · pith_short_8: V4NHCTIZ

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/V4NHCTIZ7I2NKIH6A2EIKFCZGI \
  | 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: af1a714d19fa34d520fe068885145932223275303a479f29a6569add3d10a8c4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3944e428e92576fe038bad3b12febbb6000302cc5e08e9c3249bc2630da26b75",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-05-16T14:48:31Z",
    "title_canon_sha256": "a7117ec1c018348272685a2541d3a37a65c3f9a98f7d18f0e22b53b0db9b402c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17022",
    "kind": "arxiv",
    "version": 1
  }
}