Pith Number

pith:6BP4HB3J

pith:2026:6BP4HB3J267XEFNSIHGREWJD6M

not attested not anchored not stored refs resolved

Construction of Non-special Divisors on Kummer Covers With Arbritary Ramification For LCP Codes

Adler Marques, Saeed Tafazolian, Yuri da Silva

Galois group actions and invariant divisors give necessary and sufficient conditions for non-speciality in Kummer extensions with arbitrary ramification.

arxiv:2605.14046 v1 · 2026-05-13 · math.AG · cs.IT · math.IT · math.NT

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Claims

C1strongest claim

Using Galois group actions and invariant divisor techniques, we establish necessary and sufficient conditions for non-speciality with no constraint on the support, yielding explicit constructions where previous methods fail.

C2weakest assumption

The Galois group actions on divisors remain sufficient to certify non-speciality for arbitrary ramification patterns without hidden exceptions or additional constraints in the three regimes covered.

C3one line summary

A Galois-invariant technique gives necessary and sufficient conditions for non-special divisors on general Kummer extensions, producing explicit LCP AG codes across three ramification regimes that meet or approach the Goppa bound.

References

16 extracted · 16 resolved · 1 Pith anchors

[1] On the existence of non-special divisors of degreegandg−1 in algebraic function fields overF q, 2006

[2] On linear complementary pairs of algebraic geometry codes over finite fields, 2024

[3] On linear complementary pairs of codes, 2018

[4] Linear complementary dual codes and linear complementary pairs of AG codes in function fields, 2025

[5] On generalized Weierstrass Semigroups in arbi- trary Kummer extensions ofF q(x), 2026

Receipt and verification

First computed	2026-05-17T23:39:12.693435Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f05fc38769d7bf7215b241cd125923f30f7fde707566925008f5e53c96ed1b72

Aliases

arxiv: 2605.14046 · arxiv_version: 2605.14046v1 · doi: 10.48550/arxiv.2605.14046 · pith_short_12: 6BP4HB3J267X · pith_short_16: 6BP4HB3J267XEFNS · pith_short_8: 6BP4HB3J

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/6BP4HB3J267XEFNSIHGREWJD6M \
  | 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: f05fc38769d7bf7215b241cd125923f30f7fde707566925008f5e53c96ed1b72

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "231de233d9ca15c59d2f778e1dd2fd0de17a0845f92f7451b271d2434ef3109b",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-05-13T19:08:10Z",
    "title_canon_sha256": "947944391e95fae0a7c7dcd29b71f176509554059329a7b5d3ba69a30a17b779"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14046",
    "kind": "arxiv",
    "version": 1
  }
}