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$\ell$-CYCLOTOMIC COSETS MODULO $m$
Keywords:
cyclotomic cosets, $\ell$-mapping, cyclic codesDOI:
https://doi.org/10.17654/0972555522001Abstract
Let $p_1, p_2, p_3, p_4$ and $\ell$ be distinct primes. Let $m=\prod_{i=1}^4 p_i^{\beta_i}$, where at least two of $\beta_i$ 's are nonzero positive integers. In this paper, the $\lambda$-mapping is used to obtain all the $\ell$-cyclotomic cosets modulo $m$. Then, it is shown that it is easy to count these $\ell$-cyclotomic cosets with the help of $\lambda$-mapping and we observed that the results obtained in $[1-4,6]$ and [7] on $\ell$-cyclotomic cosets modulo $m$ are the simple corollaries to the results obtained in the paper.
Received: September 4, 2021
Accepted: November 1, 2021
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