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pith:ADJKPKXU

pith:2026:ADJKPKXUTGVNOEUA7HA7YFIN6O

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Function-Correction with Optimal Data Protection for the General Hamming Code Membership

Adityawardhan Yadava, Anjana A. Mahesh, Swaraj Sharma Durgi

Bent Boolean functions deliver optimal parity assignments for single-error-correcting function-correcting codes on the general Hamming code membership function when the length parameter is even.

arxiv:2605.14023 v1 · 2026-05-13 · cs.IT · math.IT

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Claims

C1strongest claim

Eigenvectors corresponding to the minimum eigenvalue of these graphs are shown to directly yield optimal parity assignments. We reduce the problem of finding these eigenvectors to an optimization problem involving moments of the Walsh coefficients of a related function, which we solve for even n by deriving a tight lower bound shown to be attained by bent functions, establishing a precise connection between optimal SEFCC design and bent Boolean functions.

C2weakest assumption

The distance-3 codeword graph is shown to induce a connected bipartite structure for all n≥2, which is exploited to develop a systematic SEFCC construction achieving the largest possible minimum distance of 2.

C3one line summary

A construction for optimal SEFCCs on the Hamming code membership function is given by reducing distance-2 pair minimization to a max-cut problem solved via eigenvectors of distance-4 graphs, with optimality for even n attained by bent functions.

References

14 extracted · 14 resolved · 0 Pith anchors

[1] A. Lenz, R. Bitar, A. Wachter-Zeh, and E. Yaakobi, “Function-correcting codes,”IEEE Trans. Inf. Theory, vol. 69, no. 9, pp. 5604–5618, 2023 2023

[2] Optimal redundancy of function-correcting codes 2025

[3] R. Premlal and B. S. Rajan, “On Function-Correcting Codes,” in IEEE Transactions on Information Theory, vol. 71, no. 8, pp. 5884-5897

[4] Function-correcting codes for symbol-pair read channels, 2024

[5] Function-correcting codes forb-symbol read channels 2025

Formal links

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Receipt and verification

First computed	2026-05-17T23:39:12.920750Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

00d2a7aaf499aad71280f9c1fc150df38d3557d688e3342ee2ad19ea82c67a54

Aliases

arxiv: 2605.14023 · arxiv_version: 2605.14023v1 · doi: 10.48550/arxiv.2605.14023 · pith_short_12: ADJKPKXUTGVN · pith_short_16: ADJKPKXUTGVNOEUA · pith_short_8: ADJKPKXU

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ADJKPKXUTGVNOEUA7HA7YFIN6O \
  | 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: 00d2a7aaf499aad71280f9c1fc150df38d3557d688e3342ee2ad19ea82c67a54

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8233793005bdb79b35beaa0dcf8ace05f90e9a6e32ffe5a2aec1cb0d28fda4e0",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-05-13T18:35:53Z",
    "title_canon_sha256": "d64e8841c954cc03fe90bab0a9b6c04b424dba47d8ebb9bac443e4621b505df6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14023",
    "kind": "arxiv",
    "version": 1
  }
}