A class of systematic m‐ary single‐symbol error correcting codes
Kazuteru Namba, Eiji Fujiwara · Systems and Computers in Japan · 2001
Abstract Nowadays, m‐ary information such as postal numbers, ID numbers, telephone numbers, and book numbers is being widely used. Increasing the reliability of such information is very important. Single‐symbol error correcting codes for such m‐ary information (m>2) proposed in the past have some limitations. For example, AN codes are nonsystematic, and Hamming codes cannot be constructed over integer rings in which the base is other than prime numbers or power multiples of prime numbers. This paper presents a new class of systematic m‐ary single‐symbol error correcting codes whose check symbols are determined under integer ring of modulo 2m and prime field, and then transformed into m‐ary symbols. This also shows that the proposed codes are superior to existing codes in terms of the code length when the base number m is not a prime or a power multiple of prime. In addition, the detection probabilities with respect to errors greater than the code function such as double symbol errors have been clarified. © 2001 Scripta Technica, Syst Comp Jpn, 32(6): 21–28, 2001