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Minimum distance and idempotent generators of minimal cyclic codes of length ${p_1}^{\alpha_1}{p_2}^{\alpha_2}{p_3}^{\alpha_3}$
| Content Provider | Directory of Open Access Journals (DOAJ) |
|---|---|
| Author | Pankaj Kumar Pinki Devi |
| Abstract | Let $ p_1, p_2, p_3, q $ be distinct primes and $ m={p_1}^{\alpha_1}{p_2}^{\alpha_2}{p_3}^{\alpha_3}$. In this paper, it is shown that the explicit expressions of primitive idempotents in the semi-simple ring $R_m = { F_q[x]}/{(x^m-1)}$ are the trace function of explicit expressions of primitive idempotents from $R_{p_i^{\alpha_i}}$. The minimal polynomials, generating polynomials and minimum distances of minimal cyclic codes of length $m$ over $F_q$ are also discussed. All the results obtained in \cite{ref[1]}, \cite{ref[4]}, \cite{ref[5]}, \cite{ref[6]}, \cite{ref[11]} and \cite{ref[14]} are simple corollaries to the results obtained in the paper. |
| Related Links | https://jacodesmath.com/index.php/jacodesmath/article/view/164 |
| Journal | Journal of Algebra Combinatorics Discrete Structures and Applications |
| Issue Number | 3 |
| Volume Number | 8 |
| e-ISSN | 2148838X |
| Language | English |
| Publisher | Yildiz Technical University |
| Publisher Date | 2021-01-01 |
| Publisher Place | Türkiye |
| Access Restriction | Open |
| Subject Keyword | Mathematics Cyclotomic Cosets, Primitive Idempotents, Cyclic Codes, Trace Function |
| Content Type | Text |
| Resource Type | Article |
| Subject | Algebra and Number Theory Discrete Mathematics and Combinatorics |
