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Determining when a truncated generalised Reed-Solomon code is Hermitian self-orthogonal

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10.1109/TIT.2022.3150277
 
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hdl:2117/368495

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Ball, Simeon MichaelMés informacióMés informacióMés informació
Vilar Algueró, RicardMés informació
Document typeArticle
Defense date2022-02-09
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Rights accessOpen Access
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder
ProjectCOMBINATORIA GEOMETRICA, ALGEBRAICA Y PROBABILISTICA (AEI-MTM2017-82166-P)
COMBINATORIA: NUEVAS TENDENCIAS Y APLICACIONES (AEI-PID2020-113082GB-I00)
Abstract
We prove that there is a Hermitian self-orthogonal k -dimensional truncated generalised Reed-Solomon code of length n¿q2 over Fq2 if and only if there is a polynomial g¿Fq2 of degree at most (q-k)q-1 such that g+gq has q2-n distinct zeros. This allows us to determine the smallest n for which there is a Hermitian self-orthogonal k -dimensional truncated generalised Reed-Solomon code of length n over Fq2 , verifying a conjecture of Grassl and Rötteler. We also provide examples of Hermitian self-orthogonal k -dimensional generalised Reed-Solomon codes of length q2+1 over Fq2 , for k=q-1 and q an odd power of two.
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© 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works
CitationBall, S.; Vilar, R. Determining when a truncated generalised Reed-Solomon code is Hermitian self-orthogonal. "IEEE transactions on information theory", 9 Febrer 2022, vol. 68, núm. 6, p. 3796-3805. 
URIhttp://hdl.handle.net/2117/368495
DOI10.1109/TIT.2022.3150277
ISSN1557-9654
Publisher versionhttps://ieeexplore.ieee.org/document/9709260
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