Pith Number

pith:7XX3DUNB

pith:2026:7XX3DUNBBO4N7JYHRNUICPVXBF

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Nonexistence of certain classes of generalized bent functions: Revisiting the element partition method

Shi Ying, Yingpu Deng

The element partition method establishes nonexistence of generalized bent functions of type [n, 2 p1^e1 p2^e2] and type [1, 2·3^a·7^b].

arxiv:2605.13558 v1 · 2026-05-13 · math.CO · math.NT

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Claims

C1strongest claim

We obtain new nonexistence results of two classes of generalized bent functions from Z_q^n to Z_q (called type [n,q]). The first class ... where q=2 p1^e1 p2^e2 ... For the second class, we extend the idea of the element partition method and prove the nonexistence of generalized bent functions of type [1,2·3^a·7^b].

C2weakest assumption

That the element partition method, when applied to the cited results of Feng et al., produces a contradiction for the stated parameter ranges without hidden assumptions on the character sums or on the distribution of elements in the ring Z_q.

C3one line summary

Nonexistence is shown for generalized bent functions from Z_q^n to Z_q when q = 2 p1^e1 p2^e2 and when n=1 and q=2·3^a·7^b.

References

30 extracted · 30 resolved · 0 Pith anchors

[1] Fermat quotients for composite moduli.J 1997

[2] Bruce C. Berndt, Ronald J. Evans, and Kenneth S. Williams.Gauss and Jacobi sums. Canadian Mathematical Society Series of Monographs and Advanced Texts. John Wi- ley & Sons, Inc., New York, 1998. A Wil 1998

[3] Four decades of research on bent functions.Des 2016

[4] Dorais and Dominic Klyve 2011

[5] Non-existence of some generalized bent functions 2003

Receipt and verification

First computed	2026-05-18T02:44:23.553497Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fdefb1d1a10bb8dfa7078b68813eb7095bcc4a9b4bc247c7e34fb3111182627f

Aliases

arxiv: 2605.13558 · arxiv_version: 2605.13558v1 · doi: 10.48550/arxiv.2605.13558 · pith_short_12: 7XX3DUNBBO4N · pith_short_16: 7XX3DUNBBO4N7JYH · pith_short_8: 7XX3DUNB

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/7XX3DUNBBO4N7JYHRNUICPVXBF \
  | 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: fdefb1d1a10bb8dfa7078b68813eb7095bcc4a9b4bc247c7e34fb3111182627f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e4551697fd2979b8d46dcafe50e37919440afdef4aff5261064cc59a54325793",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-13T14:00:15Z",
    "title_canon_sha256": "e9f1c8df1b30268e268ee3366dae2c368bdd17c274a1b1fdd07305f705c786e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13558",
    "kind": "arxiv",
    "version": 1
  }
}