Minimal cyclic codes of length \(p^{n} q\).
Explicit expressions for all the \(3n+2\) primitive idempotents in the ring \(R_{p^nq}= \text{GF} (l)[x]/(x^{p^nq}-1)\), where \(p\), \(q\), \(l\) are distinct odd primes satisfying some conditions, are derived. The dimension, generating polynomials and minimum distance of the minimal cyclic codes of length \(p^nq\) are also discussed. As an example, all the ternary minimal cyclic codes of length 35 are described. See also the corrigendum [ibid. 18, No. 4, 863 (2012; Zbl 1247.94048)].
scientific article; zbMATH DE number 2005892