Abstract
An algebraic representation of affine MDS-codes and of mutually orthogonal Latin squares (MOLS) is given by introducing the term of a partial ternary. The extension respectively lengthening of partial ternaries, MDS-codes and MOLS is discussed.
Similar content being viewed by others
References
Belousov, V.D.: Systems of Quasigroups with Generalised Identities, Usp. Mat. Nauk., 20 (1965), No. 1 (121), 74–146. Russian Math. Surveys 20 (1965), 73–143.
Bruck, R.H.: Finite Nets, I. Numerical Invariants, Can. J. Math., 3 (1951), 94–107.
Bruck, R.H.: Finite Nets, II. Uniqueness and Imbedding, Pac. J. Math., 13 (1963), 421–457.
Dénes, J. /Keedwell, A.D.: Latin Squares and their Applications, Akadémiai Kiadó, Budapest, 1974.
Heise, W. /Quattrocchi, P.: Informations- und Codierungstheorie, 2. Auflage, Springer Verlag, Berlin, Heidelberg, 1989.
Karzel, H. /Maxson, C.J.: Affine MDS-Codes on Groups, J. Geom., 47 (1993), 65–76.
Lingenberg, R.: Grundlagen der Geometrie 1, Bibliographisches Institut, Mannheim, Wien, Zürich, 1969.
MacWilliams, F.J. /Sloane, N.J.A.: The Theory of Error-Correcting Codes, North-Holland, Amsterdam, New York, Oxford, 1977.
Pickert, G.: Projektive Ebenen, 2. Auflage, Springer-Verlag, Berlin, Heidelberg, New York, 1975.
Sade, A.: Groupoïdes orthogonaux, Publ. Math. Debrecen, 5 (1958), 229–240.
Skornyakov, L.A.: Natural Domains of Veblen-Wedderburn Projective Planes, Izv. Akad. Nauk SSSR, Ser. Mat. 13 (1949), 447–472. AMS Transl. Ser. 1, 1 (1962), 15–50.
Zhang, L.: On the Maximum Number of Orthogonal Latin Squares I., Shuxue Jinzhan, 6 (1963), 201–204. Private Translation.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Quistorff, J. Algebraic representation of affine MDS-codes and mutually orthogonal Latin squares. J Geom 61, 155–163 (1998). https://doi.org/10.1007/BF01237503
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01237503