Simultaneous Error-Correction and Burst-Error Detection Using Binary Linear Cyclic Codes

This paper considers the problem of simultaneous error-correction and burst-error detection using binary linear cyclic codes. For certain types of teletype channels, it pays to correct random errors and to detect bursts. It is shown that the burst-error detecting capability drops by one more than the length of the largest gap in the recursion polynomial when a binary linear cyclic code is used to correct single errors. Only special cases of this result are obtained for multiple-error-correction. The single-error result is applied to develop a new criterion for primitivity of polynomials over the two-element field. The criterion depends on the largest gap in the recursion polynomial corresponding to the polynomial to be tested for primitivity.