Pith Number

pith:LKS7VNHI

pith:2026:LKS7VNHIZQS3TOXZRUSXB5IKZ7

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MUBs from bent functions

William M. Kantor

Bent functions yield complete sets of mutually unbiased bases by defining vectors as explicit linear combinations of the standard basis.

arxiv:2605.17594 v1 · 2026-05-17 · math.CO · quant-ph

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Claims

C1strongest claim

This note contains a simple construction of complete sets of MUBs, using bent functions to write the new basis vectors as explicit linear combinations of the standard basis.

C2weakest assumption

That the algebraic properties of bent functions (flat Fourier spectrum over the appropriate field or ring) are sufficient to guarantee the constant-magnitude inner-product condition between distinct bases when the vectors are formed as the indicated linear combinations.

C3one line summary

A construction of complete sets of MUBs in which bent functions define explicit linear combinations of standard basis vectors.

References

8 extracted · 8 resolved · 0 Pith anchors

[1] S. Bandyopadhyay, P. O. Boykin, V. Roychowdhury and F. Vatan, A new proof for the existence of mutually unbiased bases. Algorithmica 34 (2002) 512--528 2002

[2] A. R. Calderbank, P. J. Cameron, W. M. Kantor and J. J. Seidel, _4 --Kerdock codes, orthogonal spreads, and extremal Euclidean line-sets. Proc. LMS 75 (1997) 436–480 1997

[3] R. S. Coulter and R. W. Matthews, Planar functions and planes of Lenz-Barlotti class II. Des. Codes Crypt. 10 (1997) 167--184 1997

[4] P. Dembowski, Finite Geometries. Springer, Berlin-Heidelberg-NY 1968 1968

[5] W. M. Kantor, MUBs and affine planes. J. Mathematical Physics 53 (2012) 032204 2012

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-20T00:04:47.714976Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5aa5fab4e8cc25b9baf98d2570f50acfc0cce22e5cfbc70fa0913fc600e5e3d4

Aliases

arxiv: 2605.17594 · arxiv_version: 2605.17594v1 · doi: 10.48550/arxiv.2605.17594 · pith_short_12: LKS7VNHIZQS3 · pith_short_16: LKS7VNHIZQS3TOXZ · pith_short_8: LKS7VNHI

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/LKS7VNHIZQS3TOXZRUSXB5IKZ7 \
  | 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: 5aa5fab4e8cc25b9baf98d2570f50acfc0cce22e5cfbc70fa0913fc600e5e3d4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "96704b6c40fe4be8d91fcdad82a6cf13c5b5a85ebc30ab023a45680e13568b36",
    "cross_cats_sorted": [
      "quant-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-17T18:45:43Z",
    "title_canon_sha256": "72bce8280d61f840497bf06d2348f9d5bd4d37622347282df73f30072efded56"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17594",
    "kind": "arxiv",
    "version": 1
  }
}