On the minimum average distance of binary codes: linear programming approach

Lower bounds on the minimum average distance of binary codes

Let β(n,M) denote the minimum average Hamming distance of a binary code of length n and cardinality M. In this paper we consider lower bounds on β(n,M). All the known lower bounds on β(n,M) are useful when M is at least of size about 2n−1/n. We derive new lower bounds which give good estimations when size of M is about n. These bounds are obtained using linear programming approach. In particula...

Linear Binary Error Correcting Codes with Specified Minimum Hamming Distance

On the Minimum Distance of Non Binary LDPC Codes

Minimum distance is an important parameter of a linear error correcting code. For improved performance of binary Low Density Parity Check (LDPC) codes, we need to have the minimum distance grow fast with n, the codelength. However, the best we can hope for is a linear growth in dmin with n. For binary LDPC codes, the necessary and sufficient conditions on the LDPC ensemble parameters, to ensure...

Minimum Distance of Binary Nonlinear Codes∗

A binary nonlinear code can be represented as the union of cosets of a binary linear subcode. Using this representation, new algorithms methods to compute the minimum Hamming weight and distance are presented. The performance of these algorithms is also studied.

on the effect of linear & non-linear texts on students comprehension and recalling

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