Sobre códigos corretores de erros

Abstract

In this work we discuss two main issues. In the first part, we developed two errorcorrecting codes, classified as shortened Hamming codes, Gham(n) and BP(n). These codes are optimal for Hamming distance 3, that is, are able to correct 1 error. We call optimal codes, the codes that have the largest number of codewords, given a codeword length n and a distance Hamming d. We present the recursive constructions of the Gham(n) and BP(n) and their encoding and decoding algorithms with complexity O(n). In the second part, we discuss the construction of Variable Lenght Error Correcting Codes (VLECC) and show that their cost may be lower than the corresponding fixed length code, even when the frequency distribution of the symbols to be encoded is uniform