Binary Fuzzy Codes and Some Properties of Hamming Distance of Fuzzy Codes

In this paper, we discussed binary fuzzy codes over a vector space F_2^n\; by relating classical codes with the probability of a binary symmetric channel (BSC) for receiving a sent codeword correctly. We used the weight of error patterns between a received word and the possible sent codewords to define fuzzy words over n -dimensional vector space F_2^n , and used it to define binary fuzzy codes. We also added some properties of Hamming distance of binary fuzzy codes, and the bounds of a Hamming distance of binary fuzzy codes for p=1/r , where r\geqslant 3 , and r\in \mathbbZ^+ , are determined. Finding Hamming distance of binary fuzzy codes is used for decoding sent messages on a BSC.