Pith Number

pith:YV2GB7J4

pith:2025:YV2GB7J4XOXWON2JG4Z2KTV5CD

not attested not anchored not stored refs pending

Systematic Constructions of Complementary Sets and Hadamard Matrices from Circulant Operator

Piyush Priyanshu, Subhabrata Paul, Sudhan Majhi

Arbitrary Hadamard matrices act as seeds to generate Golay complementary sets and optimal cross-Z complementary sequence sets through circulant algebraic transformations.

arxiv:2510.12315 v3 · 2025-10-14 · eess.SP

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\usepackage{pith}
\pithnumber{YV2GB7J4XOXWON2JG4Z2KTV5CD}

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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

This work establishes a unified algebraic framework that treats arbitrary Hadamard matrices as flexible seeds to systematically generate Golay complementary sets (GCS), cross Z-complementary sets (CZCS), complete complementary codes (CCC), and optimal cross-Z complementary sequence sets (CZCSS) through algebraic transformations, providing the first generalized framework for constructing optimal CZCSS from arbitrary Hadamard seeds.

C2weakest assumption

The algebraic transformations applied to circulant Hadamard matrices of order 4 (or arbitrary order) preserve the required zero-correlation-zone properties for the resulting sequence sets at the claimed ratios (2/3 or 1/2) for arbitrary lengths.

C3one line summary

A circulant-operator framework generates binary and complex complementary sequence sets with specified ZCZ ratios and optimal parameters from arbitrary Hadamard matrix seeds.

Formal links

3 machine-checked theorem links

Receipt and verification

First computed	2026-06-25T01:17:46.879826Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c57460fd3cbbaf6737493733a54ebd10d31ee2b6b63f4a906d857b25103c235e

Aliases

arxiv: 2510.12315 · arxiv_version: 2510.12315v3 · doi: 10.48550/arxiv.2510.12315 · pith_short_12: YV2GB7J4XOXW · pith_short_16: YV2GB7J4XOXWON2J · pith_short_8: YV2GB7J4

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/YV2GB7J4XOXWON2JG4Z2KTV5CD \
  | 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: c57460fd3cbbaf6737493733a54ebd10d31ee2b6b63f4a906d857b25103c235e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9b1287c6da7ea6af70a75a7a9d97fda8b442da26a8d944df741e465d35ce0331",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "eess.SP",
    "submitted_at": "2025-10-14T09:18:23Z",
    "title_canon_sha256": "538f9b6f4d0867efa18657d3cc9bfd9268eddc2fab5de65b81fb4b76ef0be50d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.12315",
    "kind": "arxiv",
    "version": 3
  }
}