Abstract: To perform error detection and correction on a data sector, syndromes are calculated and used to determine error values and error locations. Logarithmic calculations in Galois field need to be performed to determine the error locations using the syndromes. Finite field vectors are represented as “complex” numbers of the form Az+B. An algorithm is performed using the field vectors represented as complex numbers to generate the error locations. The algorithm requires the use of logarithm calculations. The results of the logarithmic calculations are looked up in two (or more) log tables. The log tables store all the possible results of the logarithm calculations. The log tables store significantly less bits than prior art techniques, reducing the amount of storage space required by a factor of 171. Techniques for controlling accesses to the log tables in an efficient manner are also provided.

Abstract: To perform error detection and correction on a data sector, syndromes are calculated and used to determine error values and error locations. Logarithmic calculations in Galois field need to be performed to determine the error locations using the syndromes. Finite field vectors are represented as “complex” numbers of the form Az+B. An algorithm is performed using the field vectors represented as complex numbers to generate the error locations. The algorithm requires the use of logarithm calculations. The results of the logarithmic calculations are looked up in two (or more) log tables. The log tables store all the possible results of the logarithm calculations. The log tables store significantly less bits than prior art techniques, reducing the amount of storage space required by a factor of 171. Techniques for controlling accesses to the log tables in an efficient manner are also provided.

Abstract: A method and system of the present invention are directed to processing payment items at a central processing facility for a merchant with multiple merchant locations. A computer implemented method for processing payment items may involve receiving an envelope with a label wherein the envelope comprises payment items from a merchant location; wherein the label indicates to a sorter at a mail facility that the envelope is destined for a central processor and the envelope skips regular mail channels; encoding one or more of the payment items at the central processor; depositing the payment items into a single national account associated with a merchant entity, wherein the merchant entity comprises a plurality of merchant locations; clearing the payment items through one or more payor entities; and providing funds availability information to the merchant entity through an online interface.