Accession Number : AD0637475
Title : A CLASS OF SOLID-BURST ERROR-CORRECTING CODES.
Descriptive Note : Scientific rept.
Corporate Author : POLYTECHNIC INST OF BROOKLYN N Y MICROWAVE RESEARCH INST
Personal Author(s) : Schillinger,A. George
Report Date : APR 1964
Pagination or Media Count : 74
Abstract : An efficient class of codes which correct errors in adjacent digits (solid bursts) is derived. Several properties of polynomials over GF(2) are found and these lead to the choice of generator polynomials g(x) of (2(m)-1, 2(m)-1-2m) cyclic codes which correct errors in 2(m-1)-1 adjacent digits or less per codeword. g(x) is shown to be of the form x(m) p(x) p(1/x) is any primitive polynomial of degree m over GF(2). For each m, the code is shown to be within one parity check of being optimum, and a simple switching circuit to implement the error-correcting process is synthesized. Albebraic properties of cyclic codes in general are considered next by examining the structure of the parity check matrix H. Among several simple relationships which are shown to exist one finds that the columns of H can be always chosen to form a cyclic group. An optimum code for a given set of correctible error patterns is one generated by an irreducible (imprimitive) polynomial. Then H and its cosets exhaust the field, they contain one error pattern each and the correctors are most efficiently utilized. Useful relationships are shown to exist among error patterns in these cosets, and the use of these results in the design of special purpose codes is illustrated. (Author)
Descriptors : (*CODING, ERRORS), CORRECTIONS, INFORMATION THEORY, POLYNOMIALS, SWITCHING CIRCUITS, MATRICES(MATHEMATICS)
Subject Categories : Cybernetics
Distribution Statement : APPROVED FOR PUBLIC RELEASE