Wong, Denis C. K.; Huey, Ang Miin A family of MDS abelian group codes. (English) Zbl 1339.94097 Far East J. Math. Sci. (FJMS) 78, No. 1, 19-27 (2013). Let \(\mathbb{F}\) be a finite field and \(G\) and abelian group. An ideal in the group algebra \(\mathbb{F}G\) can be viewed as a code over \(\mathbb{F}\). In this article the authors study the case in which \(G=\langle h | h^p=1 \rangle\times\langle k | k^q=1 \rangle\), where \(p\) and \(q\) are two distinct primes, so that \(\mathbb{F}G\) consists of \(pq\) idempotents \(e_j\). An ideal of \(\mathbb{F}G\) is a direct sum \(I_{\beta}=\oplus \mathbb{F}Ge_j\), \(e_j\in\beta\), for some subset \(\beta\). They choose suitable subsets \(\beta\) to construct codes \(I_{\beta}\) with maximum distance. They also determine the minimum distance of such \(I_{\beta}\). Reviewer: Carlos Munuera (Valladolid) Cited in 2 Documents MSC: 94B60 Other types of codes 11T71 Algebraic coding theory; cryptography (number-theoretic aspects) 94B99 Theory of error-correcting codes and error-detecting codes Keywords:abelian group codes; MDS codes; orthogonal idempotents PDFBibTeX XMLCite \textit{D. C. K. Wong} and \textit{A. M. Huey}, Far East J. Math. Sci. (FJMS) 78, No. 1, 19--27 (2013; Zbl 1339.94097) Full Text: Link