Pith Number

pith:MUYNMFKR

pith:2026:MUYNMFKRJ4EC4LVSHBQVRUUDMH

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Skew Polycyclic Codes over $\frac{\mathbb{F}_{p^m}[u]}{\langle u^t \rangle}$

Akanksha Tiwari, Ritumoni Sarma

The structure of left ideals in skew polynomial rings over finite chain rings is refined for central elements x^{np^s} - λ with nonzero constant term.

arxiv:2605.13020 v1 · 2026-05-13 · cs.IT · math.IT

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Claims

C1strongest claim

For n=1,t=3 and n=2,t=2 we give a full description of the left ideals by including certain necessary conditions that were omitted in available literature, preventing the different classes of left ideals from being mutually disjoint and in certain cases, we also compute i-th torsion codes.

C2weakest assumption

The automorphism Θ of R^t extends the automorphism θ of F_{p^m} with Θ(u)=u, and λ_0 ≠ 0 for the central element f(x) = x^{np^s} - λ.

C3one line summary

Skew polycyclic codes over the chain ring R^t are the left ideals of the quotient skew polynomial ring, with explicit structural descriptions and generators provided for central f(x) of the form x^{np^s} - lambda when n=1 or 2, plus complete listings for n=1 t=3 and n=2 t=2 that correct prior gaps.

References

32 extracted · 32 resolved · 2 Pith anchors

[1] S. Bagheri, R. M. Hesari, H. Rezaei, and K. Samei. Skew cyclic codes of lengthp s overF pm +uF pm.Iranian Journal of Science and Technology, Transactions A: Science, 46(5):1469–1475, 2022 2022

[2] D. Boucher and F. Ulmer. Linear codes using skew polynomials with automorphisms and derivations.Designs, Codes and Cryptography. An International Journal, 70:405– 431, 2014 2014

[3] B. Boudine and J. Laaouine. Polycyclic codes over Fpm[u] ⟨u2⟩ : Classification, hamming distance, and annihilators.Finite Fields and Their Applications, 88:102188, 2023. 18 2023

[4] B. Boudine, J. Laaouine, and M. E. Charkani. On the classification of ideals over R[x]/⟨f(x) ps ⟩whenR=F pm +uF pm +. . .+u nFpm.Cryptography and Communica- tions, 15(3):589–598, 2023 2023

[5] M. Boulagouaz and A. Leroy. (σ, δ)-codes.Advances in Mathematics of Communications, 7(4):463–474, 2013 2013

Cited by

1 paper in Pith

A Study Of Skew-Polycyclic Codes Over A Non-Chain Ring

Receipt and verification

First computed	2026-05-18T03:09:00.048791Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6530d615514f082e2eb2386158d28361c5c7fce4543db9e470aa2a864e6087bc

Aliases

arxiv: 2605.13020 · arxiv_version: 2605.13020v1 · doi: 10.48550/arxiv.2605.13020 · pith_short_12: MUYNMFKRJ4EC · pith_short_16: MUYNMFKRJ4EC4LVS · pith_short_8: MUYNMFKR

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/MUYNMFKRJ4EC4LVSHBQVRUUDMH \
  | 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: 6530d615514f082e2eb2386158d28361c5c7fce4543db9e470aa2a864e6087bc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "229b3c6f63fb9a5d0844b4b86055a3d78cbe47c1d902649f64ad7e96e48df126",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-05-13T05:24:15Z",
    "title_canon_sha256": "3e413130beb47536fb011285130160d0cf50056b2b38bdcf9ea0486d3a93a63a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13020",
    "kind": "arxiv",
    "version": 1
  }
}