In this paper we compute the second generalized Hamming weight of the evaluation codes associated to complete bipartite graphs. The main result depends on the minimum distance and second generalized Hamming weight of the generalized Reed-Solomon codes.

In this paper we use the Gray code representation of the genetic code C=00, U=10, G=11 and A=01 (C pairs with G, A pairs with U) to generate a sequence of genetic code-based matrices. In connection with these code-based matrices, we use the Hamming distance to generate a sequence of numerical matrices. We then further investigate the properties of the numerical matrices and show that they are d...

We revisit fuzzy neural network with a cornerstone notion of generalized hamming distance, which provides a novel and theoretically justified framework to re-interpret many useful neural network techniques in terms of fuzzy logic. In particular, we conjecture and empirically illustrate that, the celebrated batch normalization (BN) technique actually adapts the “normalized” bias such that it app...

The proposed algorithm suggests a lossless data compression with security. Input Bit stream is divided into a group of 8-bits each .Encoder deviate the available Randomly generated key according to input bit stream which results into encrypted data. Encrypted key of 64-bits is treated as unit of 4-bits each. Each 4-bits of Key will be at the Hamming distance is of Two from Deviated key. There w...

The Hamming distance function Hamn,d returns 1 on all pairs of inputs x and y that differ in at most d coordinates and returns 0 otherwise. We initiate the study of the information complexity of the Hamming distance function. We give a new optimal lower bound for the information complexity of the Hamn,d function in the small-error regime where the protocol is required to err with probability at...

Let j ≥ k ≥ 0 be integers. An `-L(j, k)-labelling of a graph G = (V , E) is a mapping φ : V → {0, 1, 2, . . . , `} such that |φ(u)−φ(v)| ≥ j if u, v are adjacent and |φ(u)−φ(v)| ≥ k if they are distance two apart. Let λj,k(G) be the smallest integer ` such that G admits an `-L(j, k)-labelling. Define λj,k(G) to be the smallest ` if G admits an `-L(j, k)-labelling with φ(V ) = {0, 1, 2, . . . , ...

We investigate relations between (+, ) vector products for binary integer functions . We show that there exists a broad class of products that are equivalent under one-to-polylog reductions to the computation of the Hamming distance. Examples include, but are not exhausted by: the dominance product, the threshold product and `2p+1 distances for constant p. Our result has the following consequen...

Hq(n, d) is defined as the graph with vertex set Zq and where two vertices are adjacent if their Hamming distance is at least d. The chromatic number of these graphs is presented for various sets of parameters (q, n, d). For the 4-colorings of the graphs H2(n, n − 1) a notion of robustness is introduced. It is based on the tolerance of swapping colors along an edge without destroying properness...

The hashing methods have attracted much attention for large scale image retrieval. Some deep hashing methods have achieved promising results by taking advantage of the better representation power of deep networks recently. However, existing deep hashing methods treat all hash bits equally. On one hand, a large number of images share the same distance to a query image because of the discrete Ham...