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On two conjectures of the duals of AMDS BCH codes.

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Title: On two conjectures of the duals of AMDS BCH codes.
Authors: Yan, Haode1 (AUTHOR) hdyan@swjtu.edu.cn
Source: Finite Fields & Their Applications. Mar2026, Vol. 111, pN.PAG-N.PAG. 1p.
Subjects: Cyclic codes, Duality theory (Mathematics), Mathematical notation, Hypothesis
Abstract: In this paper, we study the duals of BCH codes C (q , q + 1 , 3 , p − 1 2) and C (3 s , 3 s + 1 , 3 , 4). By analyzing the number of solutions to certain equations over the multiplicative subgroup U q + 1 = { x ∈ F q 2 : x q + 1 = 1 } of F q 2 ⁎ , we determine the possible weights of codewords in C (q , q + 1 , 3 , p − 1 2) ⊥ and C (3 s , 3 s + 1 , 3 , 4) ⊥ , respectively. The weight distributions of these two dual codes are derived by applying the Pless power moments. Our results provide affirmative solutions to recent conjectures. [ABSTRACT FROM AUTHOR]
Copyright of Finite Fields & Their Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
An: 191007757
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: On two conjectures of the duals of AMDS BCH codes.
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  Data: <searchLink fieldCode="AR" term="%22Yan%2C+Haode%22">Yan, Haode</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> hdyan@swjtu.edu.cn</i>
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  Data: <searchLink fieldCode="JN" term="%22Finite+Fields+%26+Their+Applications%22">Finite Fields & Their Applications</searchLink>. Mar2026, Vol. 111, pN.PAG-N.PAG. 1p.
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  Data: <searchLink fieldCode="DE" term="%22Cyclic+codes%22">Cyclic codes</searchLink><br /><searchLink fieldCode="DE" term="%22Duality+theory+%28Mathematics%29%22">Duality theory (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+notation%22">Mathematical notation</searchLink><br /><searchLink fieldCode="DE" term="%22Hypothesis%22">Hypothesis</searchLink>
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  Data: In this paper, we study the duals of BCH codes C (q , q + 1 , 3 , p − 1 2) and C (3 s , 3 s + 1 , 3 , 4). By analyzing the number of solutions to certain equations over the multiplicative subgroup U q + 1 = { x ∈ F q 2 : x q + 1 = 1 } of F q 2 ⁎ , we determine the possible weights of codewords in C (q , q + 1 , 3 , p − 1 2) ⊥ and C (3 s , 3 s + 1 , 3 , 4) ⊥ , respectively. The weight distributions of these two dual codes are derived by applying the Pless power moments. Our results provide affirmative solutions to recent conjectures. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Finite Fields & Their Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1016/j.ffa.2025.102765
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      – Code: eng
        Text: English
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        PageCount: 1
        StartPage: N.PAG
    Subjects:
      – SubjectFull: Cyclic codes
        Type: general
      – SubjectFull: Duality theory (Mathematics)
        Type: general
      – SubjectFull: Mathematical notation
        Type: general
      – SubjectFull: Hypothesis
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      – TitleFull: On two conjectures of the duals of AMDS BCH codes.
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              M: 03
              Text: Mar2026
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              Y: 2026
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