Güzeltepe, Murat; Altınel, Alev Perfect 1-error-correcting Hurwitz weight codes. (English) Zbl 1387.94114 Math. Commun. 22, No. 2, 265-272 (2017). Summary: Let \(\pi\) be a Hurwitz prime and \(p=\pi \pi^\star\). In this paper, we construct perfect 1-error-correcting codes in \(\mathcal{H}_{\pi}^n\) for every prime number \(p>3\), where \(\mathcal{H}\) denotes the set of Hurwitz integers. MSC: 94B05 Linear codes (general theory) 94B60 Other types of codes Keywords:block codes; Hurwitz distance; perfect code PDFBibTeX XMLCite \textit{M. Güzeltepe} and \textit{A. Altınel}, Math. Commun. 22, No. 2, 265--272 (2017; Zbl 1387.94114) Full Text: Link References: [1] B. Lindstr¨om, On group and nongroup perfect codes in q symbols, Math. Scand.25(1969), 149-158. · Zbl 0205.46903 [2] M. G¨uzeltepe, Codes over Hurwitz integers, Disc. Math. 313(2013), 704-714. · Zbl 1259.94069 [3] M. G¨uzeltepe, O. Heden, Perfect Mannheim, Lipschitz and Hurwitz weight codes,Math. Commun. 19(2014), 253-276. · Zbl 1369.94595 [4] R. W. Hamming, Error Detecting and Error Correcting Codes, Bell System TechnicalJournal 29(1950), 147-160. · Zbl 1402.94084 [5] O. Heden, A new construction of group and nongroup perfect codes, Information andControl 34(1977), 314-323. · Zbl 0359.94013 [6] O. Heden, M. G¨uzeltepe, On perfect 1 − E -error-correcting codes, Math. Commun.20(2015), 23-35. · Zbl 1327.94092 [7] O. Heden, M. G¨uzeltepe, Perfect 1-error-correcting Lipschitz weight codes, Math.Commun. 21(2016), 23-30. · Zbl 1369.94616 [8] C. Y. Lee, Some properties of non-binary error correcting codes, IEEE Trans. Inform.Theory 4(1958), 77-82. [9] J. Sch¨onheim, On linear and nonlinear, single-error-correcting q−nary perfect codes,Information and Control 12(1968), 23-26. · Zbl 0162.51203 [10] Y. L. Vasil’ev, On nongroup close-packed codes, Problemy Kibernetiki 8(1962), 337-339. · Zbl 0202.50305 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.