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 ...

Methods for the fast computation of Hamming distance developed for the case of large number of pairs of words are presented and discussed in the paper. The connection of this subject to some questions about intersecting sets and Hadamard designs is also considered.

When approximating binary similarity using the hamming distance between short binary hashes, we show that even if the similarity is symmetric, we can have shorter and more accurate hashes by using two distinct code maps. I.e. by approximating the similarity between x and x′ as the hamming distance between f(x) and g(x′), for two distinct binary codes f, g, rather than as the hamming distance be...

We here study Max Hamming XSAT, ie, the problem of finding two XSAT models at maximum Hamming distance. By using a recent XSAT solver as an auxiliary function, an O(1.911^n) time algorithm can be constructed, where n is the number of variables. This upper time bound can be further improved to O(1.8348^n) by introducing a new kind of branching, more directly suited for finding models at maximum ...

An alternative notion of approximation arising in cognitive psychology, bioinformatics and linguistics is that of computing a solution which is structurally close to an optimal one. That is, an approximate solution is considered good if its distance from an optimal solution is small, for a distance measure such as Hamming distance or edit distance. There has been a modicum of work on approximat...

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...

In a previous paper, we derived a recursive formula determining the weight distributions of the [n = (qm − 1)/(q − 1), n−m, 3] Hamming code H(m,q), when (m, q−1) = 1. Here q is a prime power. We note here that the formula actually holds for any positive integer m and any prime power q, without the restriction (m,q − 1) = 1.

The n-dimensional ternary Hamming space is Tn, where T = f0; 1; 2g. Three points in Tn form a line if they have in common excactly n 1 components. A subset of Tn is closed if, whenever it contains two points of a line, it contains also the third one. A generator is a set, whose closure is Tn. In this paper, we investigate several properties of closed sets and generators. Two alternative proofs ...

A well known strategy for belief revision is the use of an operator which takes as input a belief base and formula and outputs a new consistent revised belief base. Many operators require additional information such as epistemic entrenchment relations, system of spheres, faithful orderings, subformulae relation, etc. However, in many applications this extra information does not exist and all be...