Nonexistence of Order-32 Gated Costas Arrays with Blocks of Size at Most 17

Open IEEE-format preprint. Proves the shift-1 adjacent-difference obstruction for the stated two-contiguous-block diagonal-corner class and exhaustively closes the 15+17 and 16+16 splits. The result does not resolve unrestricted order-32 Costas existence. Evidence class: EXHAUSTIVE-COMPUTATION + MATHEMATICAL-PROOF.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-21
DOI
https://doi.org/10.5281/zenodo.22865915
Primary Topic
graph theory and CDMA systems
Type
preprint
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preprint

Nonexistence of Order-32 Gated Costas Arrays with Blocks of Size at Most 17

Liam D. Sparling
Zenodo (CERN European Organization for Nuclear Research)
graph theory and CDMA systems
preprint

Nonexistence of Order-32 Gated Costas Arrays with Blocks of Size at Most 17

Liam D. Sparling
preprint en

Abstract

Open IEEE-format preprint. Proves the shift-1 adjacent-difference obstruction for the stated two-contiguous-block diagonal-corner class and exhaustively closes the 15+17 and 16+16 splits. The result does not resolve unrestricted order-32 Costas existence. Evidence class: EXHAUSTIVE-COMPUTATION + MATHEMATICAL-PROOF.

Zenodo (CERN European Organization for Nuclear Research)
EM Photonics (United States) (US)
graph theory and CDMA systems
DOIOpen Access PDFOpenAlex
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Nonexistence of Order-32 Gated Costas Arrays with Blocks of Size at Most 17 — Liam D. Sparling · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS