Let A3(n, d,w) denote the maximum cardinality of a ternary code with length n, minimum distance d, and constant Hamming weight w. Methods for proving upper and lower bounds on A3(n, d,w) are presented, and a table of exact values and bounds in the range n ≤ 10 is given.

We address the problem of sketching the hamming distance of data streams. We present a new notion of sketching technique, Fixable sketches and we show that using such sketch not only we reduce the sketch size, but also restore the differences between the streams. Our contribution: For two streams with hamming distance bounded by k we show a sketch of size O(k logn) with O(logn) processing time ...

We study the effect of addition on the Hamming weight of a positive integer. Consider the first 2n positive integers, and fix an α among them. We show that if the binary representation of α consists of Θ(n) blocks of zeros and ones, then addition by α causes a constant fraction of low Hamming weight integers to become high Hamming weight integers. This result has applications in complexity theo...

introduction:  the  purpose  of  this  study  is  to  define  the  optimal  parameters  for  the  tomographic  reconstruction procedure in a routine single photon emission tomography. the hoffman brain phantom  is modified to evaluate the reconstruction method. the phantom was imaged in a 3 and 2-dimensional  conformation and the results were compared.   materials  and  methods:  the  2d  phant...

The high level of security and the fast hardware and software implementation of the Advanced Standard Encryption (AES) have made it in the first choice for many critical applications. Advanced Encryption Standard (AES) is the self-determining hardware architecture for producing crypto mechanism. In a secure transmission system, Content Addressable Memory (CAM) based transmissions always provide...

We will say that an alphabet A satisfies the extension property with respect to a weight w if every linear isomorphism between two linear codes in A that preserves w extends to a monomial transformation of A. In the 1960s MacWilliams proved that finite fields have the extension property with respect to Hamming weight. It is known that a module A has the extension property with respect to Hammin...

The paper deals with the perfect 1-error correcting codes over a finite field with q elements (briefly q-ary 1-perfect codes). We show that the orthogonal code to the q-ary non-full-rank 1-perfect code of length n = (q − 1)/(q − 1) is a q-ary constant-weight code with Hamming weight equals to qm−1 where m is any natural number not less than two. We derive necessary and sufficient conditions for...

In this note we determine the second generalized Hamming weight of the dual codes of binary doubleerror correcting BCH-codes.

We derive new estimates of the size of codes and orthogonal arrays in the ordered Hamming space (the Niederreiter-Rosenbloom-Tsfasman space). We also show that the eigenvalues of the ordered Hamming scheme, the association scheme that describes the combinatorics of the space, are given by the multivariable Krawtchouk polynomials, and establish some of their properties.

in this paper, the weighted szeged indices of cartesian product and corona product of twoconnected graphs are obtained. using the results obtained here, the weighted szeged indices ofthe hypercube of dimension n, hamming graph, c4 nanotubes, nanotorus, grid, t− fold bristled,sunlet, fan, wheel, bottleneck graphs and some classes of bridge graphs are computed.