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The q-ary Golay arrays of size \(2\times 2\times \cdots \times 2\) are standard

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Abstract

To find the non-standard binary Golay sequences of length \(2^{m}\) or theoretically prove their nonexistence are still open. It has been shown that all the standard q-ary (q even) Golay sequence pairs of length \(2^m\) can be obtained by q-ary Golay array pairs of dimension m and size \(2\times 2 \times \cdots \times 2\) of a particular algebraic normal form. We extend the appellation “standard" from sequences to arrays and call the Golay array pairs of this algebraic normal form standard. It’s natural to ask whether all the q-ary Golay array pairs of size \(2\times 2 \times \cdots \times 2\) are standard. We give a positive answer to this question.

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Funding

This study was supported by National Natural Science Foundation of China (NSERC) (Grant Nos. 62172319, U19B2021) and National Key Research and Development Program (Grant No. 2021YFA000503).

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Authors and Affiliations

  1. State Key Laboratory of Integrated Service Networks, School of Cyber Engineering, Xidian University, Xi’an, 710071, China

    Erzhong Xue & Zilong Wang

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  1. Erzhong Xue
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  2. Zilong Wang
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Correspondence to Zilong Wang.

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Communicated by J. Jedwab.

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The authors were supported in part by the National Natural Science Foundation of China under Grants 62172319 and U19B2021.

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Xue, E., Wang, Z. The q-ary Golay arrays of size \(2\times 2\times \cdots \times 2\) are standard. Des. Codes Cryptogr. 91, 2769–2778 (2023). https://doi.org/10.1007/s10623-023-01230-8

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  • DOI: https://doi.org/10.1007/s10623-023-01230-8

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