
Accession Number : AD0634989
Title : CYCLIC CODES. RESEARCH PROGRAM TO EXTEND THE THEORY OF WEIGHT DISTRIBUTION AND RELATED PROBLEMS FOR CYCLIC ERRORCORRECTING CODES AND CONSTRUCTIVE CODING THEORY.
Descriptive Note : Final rept., 1 Jun 6131 Mar 66,
Corporate Author : SYLVANIA ELECTRONIC SYSTEMSEAST WALTHAM MASS APPLIED RESEARCH LAB
Personal Author(s) : Assmus,E. F. , Jr. ; Mattson,H. F. , Jr. ; Turyn,R.
Report Date : 28 APR 1966
Pagination or Media Count : 133
Abstract : Each perfect code on q symbols which corrects e errors 'contains' a tactical configuration of type (q1) to the e th power; (e+1)(2e+1)n, where n is the block length. The HGolay codes also 'contain' in the case q=2 a closed kth order Steiner system, and for q > 2 an analogous new configuration. An error in the literature is pointed out. A lower bound on the number of inequivalent Steiner triple systems is established. Work of Lloyd and Golay on perfect codes is recast. Other necessary conditions for perfect codes are also derived. We give an updated account of previous work on weights in quadraticresidue codes, and improve on the squareroot bound on the minimum distance. The HGolay code of type (n, nk) over GF(q) is cyclic if and only if the gcd (k, q1) is 1. Minimum weights in several cyclic codes are determined. The possible isomorphism of the combinatorial designa defined by certain difference sets with identical parameters is studied. At most two of the designs considered are isomorphic. (Author)
Descriptors : (*CODING, THEORY), GROUPS(MATHEMATICS), STATISTICAL ANALYSIS
Subject Categories : Cybernetics
Distribution Statement : APPROVED FOR PUBLIC RELEASE