Publication: Generator Matrices of Quasi-cyclic Codes over Extension Fields Obtained from Gröbner Basis
Generator Matrices of Quasi-cyclic Codes over Extension Fields Obtained from Gröbner Basis
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Chimal-Dzul, H., Lieb, J., & Rosenthal, J. (2022). Generator Matrices of Quasi-cyclic Codes over Extension Fields Obtained from Gröbner Basis. IFAC-PapersOnLine, 55(30), 61–66. https://doi.org/10.1016/j.ifacol.2022.11.029
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Quasi-cyclic codes over finite fields are an important class of linear block codes. A fundamental problem in the theory of these codes is to describe their algebraic structure. In this paper it is shown that every quasi-cyclic code is the subfield code and the trace code of a quasi-cyclic code over an extension field. The latter is defined by a parity check matrix obtained from a spectral analysis of a reduced Gröbner basis of the former. Moreover, it is shown that the quasi-cyclic code over the extension field and the one under consi
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- Chimal-Dzul, Henry
- Lieb, Julia
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Chimal-Dzul, H., Lieb, J., & Rosenthal, J. (2022). Generator Matrices of Quasi-cyclic Codes over Extension Fields Obtained from Gröbner Basis. IFAC-PapersOnLine, 55(30), 61–66. https://doi.org/10.1016/j.ifacol.2022.11.029
