Laaksonen, Antti; Östergård, Patric R. J. New lower bounds on \(q\)-ary error-correcting codes. (English) Zbl 1419.94093 Cryptogr. Commun. 11, No. 5, 881-889 (2019). Summary: Let \( A_q (n, d)\) denote the maximum size of a \(q\)-ary code with length \(n\)and minimum distance \(d\). For most values of \(n\)and \(d\), only lower and upper bounds on \(A_q (n, d)\) are known. In this paper new lower bounds on and updated tables of \( A_q (n, d)\) for \(q \in\{3, 4, 5\}\) are presented. The new bounds are obtained through an extensive computer search for codes with prescribed groups of automorphisms. Groups that act transitively on the (coordinate,value) pairs as well as groups with certain other closely related actions are considered. MSC: 94B65 Bounds on codes 68P30 Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) (aspects in computer science) Keywords:automorphism groups; bounds on codes; error-correcting codes; transitive groups Software:Cliquer PDFBibTeX XMLCite \textit{A. Laaksonen} and \textit{P. R. J. Östergård}, Cryptogr. Commun. 11, No. 5, 881--889 (2019; Zbl 1419.94093) Full Text: DOI References: [1] Agrell, E., Vardy, A., Zeger, K.: A table of upper bounds for binary codes. IEEE Trans. Inform. Theory 47, 3004-3006 (2001) · Zbl 1003.94045 [2] Bellini, E., Guerrini, E., Sala, M.: Some bounds on the size of codes. IEEE Trans. Inform. Theory 60, 1475-1480 (2014) · Zbl 1360.94460 [3] Blokhuis, A., Brouwer, A.E.: Small additive quaternary codes. Eur. J. Combin. 25, 161-167 (2004) · Zbl 1046.94012 [4] Bogdanova, G.T., Brouwer, A.E., Kapralov, S.N., Östergård, P.R.J.: Error-correcting codes over an alphabet of four elements. Des. 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