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Equivalence of constacyclic codes with shift constants of different orders

Λεπτομέρειες βιβλιογραφικής εγγραφής
Τίτλος: Equivalence of constacyclic codes with shift constants of different orders
Πηγή: Designs Codes and Cryptography. 93(1):79-93
Στοιχεία εκδότη: 2025.
Έτος έκδοσης: 2025
Θεματικοί όροι: isometric equivalence, Constacyclic code, monomial equivalence, cyclic code, new linear code
Περιγραφή: Let a and b be two non-zero elements of a finite field Fq , where q > 2. It has been shown that if a and b have the same multiplicative order in Fq , then the families of a-constacyclic and b-constacyclic codes over Fq are monomially equivalent. In this paper, we investigate the monomial equivalence of a-constacyclic and b-constacyclic codes when a and b have distinct multiplicative orders. We present novel conditions for establishing monomial equivalence in such constacyclic codes, surpassing previous methods of determining monomially equivalent constacyclic and cyclic codes. As an application, we use these results to search for new linear codes more systematically. In particular, we present more than 70 new record-breaking linear codes over various finite fields, as well as new binary quantum codes.
Τύπος εγγράφου: Article
Γλώσσα: English
ISSN: 0925-1022
DOI: 10.1007/s10623-024-01512-910.1007/s10623-024-01512-9
Αριθμός Καταχώρησης: edsair.dris...02463..6d68f2566649e2cd428b1099d984eb15
Βάση Δεδομένων: OpenAIRE
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  – Url: https://dx.doi.org/doi:10.1007/s10623-024-01512-910.1007/s10623-024-01512-9
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  Data: Equivalence of constacyclic codes with shift constants of different orders
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  Data: <i>Designs Codes and Cryptography</i>. 93(1):79-93
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  Data: 2025.
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  Data: <searchLink fieldCode="DE" term="%22isometric+equivalence%22">isometric equivalence</searchLink><br /><searchLink fieldCode="DE" term="%22Constacyclic+code%22">Constacyclic code</searchLink><br /><searchLink fieldCode="DE" term="%22monomial+equivalence%22">monomial equivalence</searchLink><br /><searchLink fieldCode="DE" term="%22cyclic+code%22">cyclic code</searchLink><br /><searchLink fieldCode="DE" term="%22new+linear+code%22">new linear code</searchLink>
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  Data: Let a and b be two non-zero elements of a finite field Fq , where q > 2. It has been shown that if a and b have the same multiplicative order in Fq , then the families of a-constacyclic and b-constacyclic codes over Fq are monomially equivalent. In this paper, we investigate the monomial equivalence of a-constacyclic and b-constacyclic codes when a and b have distinct multiplicative orders. We present novel conditions for establishing monomial equivalence in such constacyclic codes, surpassing previous methods of determining monomially equivalent constacyclic and cyclic codes. As an application, we use these results to search for new linear codes more systematically. In particular, we present more than 70 new record-breaking linear codes over various finite fields, as well as new binary quantum codes.
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  Data: 10.1007/s10623-024-01512-910.1007/s10623-024-01512-9
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      – SubjectFull: isometric equivalence
        Type: general
      – SubjectFull: Constacyclic code
        Type: general
      – SubjectFull: monomial equivalence
        Type: general
      – SubjectFull: cyclic code
        Type: general
      – SubjectFull: new linear code
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