Pith Number

pith:U66ICHW3

pith:2025:U66ICHW3PANTQXRFIZY4YSBIRX

not attested not anchored not stored refs resolved

A Generic Construction of $q$-ary Near-MDS Codes Supporting 2-Designs with Lengths Beyond $q+1$

Chunming Tang, Dongchun Han, Hao Chen, Hengfeng Liu, Zhengchun Zhou

q-ary NMDS codes that support 2-designs can be built generically with lengths exceeding q+1

arxiv:2506.16793 v3 · 2025-06-20 · math.CO · cs.IT · math.IT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{U66ICHW3PANTQXRFIZY4YSBIRX}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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

We present the first generic construction of q-ary NMDS codes supporting 2-designs with lengths exceeding q + 1, resulting in an infinite family of such codes along with their weight distributions.

C2weakest assumption

The claimed new connections between elliptic curve codes, finite abelian groups, subset sums, and combinatorial designs actually produce NMDS codes that support 2-designs for lengths beyond q+1 (abstract, paragraph on method).

C3one line summary

A generic construction produces an infinite family of q-ary NMDS codes supporting 2-designs with lengths exceeding q+1 and explicit weight distributions.

References

62 extracted · 62 resolved · 0 Pith anchors

[1] E.F. Assmus Jr., H.F. Mattson Jr., New 5-designs, J. Combinat. Theory 6 (2) (1969) 122–151. 26 1969

[2] T. Beth, D. Jungnickel, H. Lenz, Design Theory, 2nd ed., Cambridge Univ. Press, Cambridge, UK, 1999 1999

[3] De Boer, Almost MDS codes, Des 1969

[4] Colbourn, CRC Handbook of Combinatorial Designs, CRC Press, Boca Raton, FL 2010

[5] Ding, Infinite families of 3-designs from a type of five-weight code, Des 2018

Receipt and verification

First computed	2026-06-09T02:07:04.596173Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a7bc811edb781b385e254671cc48288dcdccadc203d07413e26ebe00dc23397d

Aliases

arxiv: 2506.16793 · arxiv_version: 2506.16793v3 · doi: 10.48550/arxiv.2506.16793 · pith_short_12: U66ICHW3PANT · pith_short_16: U66ICHW3PANTQXRF · pith_short_8: U66ICHW3

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/U66ICHW3PANTQXRFIZY4YSBIRX \
  | 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: a7bc811edb781b385e254671cc48288dcdccadc203d07413e26ebe00dc23397d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a5a46261aed52491e1765f88b8dba6d6ed8d4bb8a54ab94596084a082c8f6d6",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-06-20T07:17:17Z",
    "title_canon_sha256": "de7a0bdd4e28a4c0d72af87da50fcc97760af8f3fa3a726f838cbca5ffd611aa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.16793",
    "kind": "arxiv",
    "version": 3
  }
}