A CLASS OF SOLID-BURST ERROR-CORRECTING CODES.
POLYTECHNIC INST OF BROOKLYN N Y MICROWAVE RESEARCH INST
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An efficient class of codes which correct errors in adjacent digits solid bursts is derived. Several properties of polynomials over GF2 are found and these lead to the choice of generator polynomials gx of 2m-1, 2m-1-2m cyclic codes which correct errors in 2m-1-1 adjacent digits or less per codeword. gx is shown to be of the form xm px p1x is any primitive polynomial of degree m over GF2. 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