Integer Codes Correcting Single Errors and Detecting Double Adjacent Errors

This paper presents two classes of integer codes called integer SEC-(DAED)${}_b$ codes and integer SEC-DAED codes. The first class of codes can correct all single errors and detect all double adjacent (DA) errors within a $b$-bit byte, while the second class of codes has the ability to correct all single errors and detect all DA errors. Both classes of codes are defined over integer rings and are generated by computer search. To evaluate the performance of the proposed codes, we analyze the probability of incorrect decoding for different error rates. In addition, the paper shows that the proposed codes have a slightly higher redundancy than linear SEC-DAED codes, but also a much simpler decoding algorithm.