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

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Linear Binary Error Correcting Codes with Specified Minimum Hamming Distance

Trellis-Coded Quantization Based on Maximum-Hamming-Distance Binary Codes

Most design approaches for trellis-coded quantization take advantage of the duality of trellis-coded quantization with trellis-coded modulation, and use the same empiricallyfound convolutional codes to label the trellis branches. This letter presents an alternative approach that instead takes advantage of maximum-Hamming-distance convolutional codes. The proposed source codes are shown to be co...

Hamming codes and some theory of linear error correcting codes

The topic is how to reduce the error of communication in the presence of noise. Block encoding is an expansion function from a block of plaintext alphabet symbols to a block of communication alphabet symbols where the block lengths are k and n respectively, and k ≤ n. Without loss of generality we consider both alphabets to be bit strings. The notation for an i length bit string is σ ∈ { 0, 1 }...

Computation of Minimum Hamming Weight for Linear Codes

In this paper, we consider the minimum Hamming weight for linear codes over special finite quasi-Frobenius rings. Furthermore, we obtain minimal free $R$-submodules of a finite quasi-Frobenius ring $R$  which contain a linear code and derive the relation between their minimum Hamming weights. Finally, we suggest an algorithm that computes this weight using the Grobner basis and we show that und...