Constructing Proper Codes for Error Detection
Torleiv Kløve · IEEE Transactions on Information Theory · 2009
It is shown that for any alphabet size$q$and any code size$M$, there exist proper codes for error detection on a$q$-ary symmetric channel for all sufficiently large lengths. The stronger conditionzero-strong propercode is defined. It is shown that such codes can only exist for$q$dividing$M$, and if this is the case they are shown to exist for sufficiently large lengths. The existence proofs are constructive.