Codes of Length Two Correcting Single Errors of Limited Size II

摘要

Linear codes of length 2 over the integers modulo some integer q that can correct single errors of limited size are considered. A code can be determined by a check pair of integers. The errors e considered are in the range - μ ≤ e ≤ λ, such a code can only exist for q sufficiently large. The main content of this note is to make this statement precise, that is, to determine "q sufficiently large" in terms of the integers -μ and λ.