The les association scheme
In this paper we undertake a study of the Lee scheme. We give in this context a new proof of Bassalygo's generalization of Lloyd Theorem, and an asymptotic estimate of the number of zeroes of the Lloyd polynomial.
We obtain a recursion on the Lee composition distribution of the translates of a code and deduce from that an upper bound on the covering radius of a code.
We give an algebraic characterization of T-designs in this scheme, which shows that they form a special class of orthogonal arrays.
KeywordsOrthogonal Array Association Scheme Perfect Code Weight Enumerator Transitive Graph
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- G. ANDREWS "The theory of partitions" Addison Wesley Encyclopedia of Math and its applications.Google Scholar
- J. ASTOLA "The theory of Lee codes" Research report 1982 University of Lappeenranta, Finland.Google Scholar
- E. BANNAI and T. ITO "Algebraic combinatorics". Benjamin Cummings.Google Scholar
- L.A. BASSALYGO "A necessary condition for the existence of perfect codes in the Lee-metric" Mat. Zametki 15, p. 313–320, 1974.Google Scholar
- E.R. BERLEKAMP "Algebraic coding theory" Revised 1984 edition Aegean Park Press.Google Scholar
- N. BIGGS "Finite groups of automorphisms". Cambridge University Press.Google Scholar
- R.C. BOSE and D.M. MESNER (1959) "On linear associative algebras corresponding to association schemes of partially balanced designs" Ann. Math. Statist. 10 p. 21–38.Google Scholar
- P. DELSARTE "Four fundamental parameters of a code and their combinarorial significance" Info and Control 1973, 23, p. 407–438.Google Scholar
- P. DELSARTE "An algebraic approach to the association schemes of coding theory" Philips Res. Rpts. Suppl 1973 No 10.Google Scholar
- S.W. GOLOMB and L.R. WELCH "Perfect codes in the Lee metric and the packing of polyominoes" SIAM J. Appl. Math. Vol 18 No 2 pp. 302–317, 1970.Google Scholar
- S.W. GOLOMB and L.R. WELCH "Algebraic coding and the Lee metric" in Error correcting codes. H.B. MANN ed. p. 175–194 Wiley N.Y. 1968.Google Scholar
- C.Y. LEE "Some properties of non binary error correcting codes" IEEE transactions on Information Theory. IT-4 p. 77–82.Google Scholar
- F.J. MAC WILLIAMS (1961) Doctoral Disertation Harvard University unpublished.Google Scholar
- F.J. MAC WILLIAMS and N.J.A. SLOANE "The theory of error correcting codes" North Holland.Google Scholar
- P. SOLE "On the parameters of Lee Codes" in preparation.Google Scholar
- H. TARNANEN "An approach to constant weight and Lee codes by using the methods of association schemes" Thesis Turku University 1982. Finland.Google Scholar