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

Abstract

In this paper, we discussed binary fuzzy codes over a vector space F2n 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 F2n, 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⩾3, and r∈Z+, are determined. Finding Hamming distance of binary fuzzy codes is used for decoding sent messages on a BSC.

Keywords

• classical codes
• binary fuzzy codes
• fuzzy space and hamming distance