Open AccessOptimal Quinary Cyclic Codes with Minimum Distance Four
Author(s) -
Fan Jinmei,
Zhang Yanhai
Publication year - 2020
Publication title -
chinese journal of electronics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.267
H-Index - 25
eISSN - 2075-5597
pISSN - 1022-4653
DOI - 10.1049/cje.2020.02.011
Subject(s) - quinary , finite field , mathematics , generator (circuit theory) , polynomial , field (mathematics) , discrete mathematics , pure mathematics , mathematical analysis , physics , power (physics) , materials science , alloy , quantum mechanics , composite material
The necessary and sufficient condition for the quinary cyclic codes with generator polynomial ( x + 1) m α ( x ) m α e ( x ) to have parameters [5 m ‐ 1,5 m ‐ 2 m ‐ 2,4] is provided by analyzing solutions of certain equations over the finite field F 5 m . And thus several classes of new optimal quinary cyclic codes with the same parameters and generator polynomial are constructed based on analyzing irreducible factors of certain polynomials with low degrees over finite fields.