Showing papers by "Jack K. Wolf published in 1965"
TL;DR: A class of codes is described having checkMatrices which are the tensor product of the check matrices of known nonbinary codes and binary codes which correct random bursts of errors and bursts of burst of errors.
Abstract: A class of codes is described having check matrices which are the tensor product of the check matrices of known nonbinary codes and binary codes. The error-correction, error-detection, and error-location capabilities of these codes are specified in terms of the properties of the component codes. The construction procedure allows for a class of codes with a wide variety of redundancies and error-control capabilities. Examples are given of codes from this class which correct random bursts of errors and bursts of bursts of errors.
109 citations
TL;DR: P parity check matrix for resultant code number of binary information digits in resultant code m number of check symbols in C2 n block length of resultant code P parity cheek matrix for C2 ~/ii i-jth element of F p number of Check digits in code C1
Abstract: aj constant b width of burst of errors C1 binary error-detecting code C2 nonbinary error-correcting code d minimum distance e number of random errors 8¢ class of correctable errors for C2 8d class of detectable errors for C1 I t parity check matrix for resultant code k number of binary information digits in resultant code m number of check symbols in C2 n block length of resultant code P parity cheek matrix for C1 p~ /th column of P r number of binary check digits in resultant code S syndrome Si ith component of syndrome (considered as an element of GF(2 ~)) s number of sub-blocks in resultant code: also, total number of symbols in code C2 t number of digits per sub-block in resultant code: also, total number of digits in code C~ W primitive element of GF(2 s) xl unknown dement of GF(2 °) a element of GF(26) F parity check matrix for C2 ~/ii i-jth element of F p number of check digits in code C1
37 citations