In this paper, we discovered that RC4 can generate colliding key pairs with various hamming distances, other than those found by Matsui (with hamming distance one), and by Chen and Miyaji (with hamming distance three). We formalized RC4 colliding key pairs into two large patterns, namely, Transitional pattern and Self-Absorbing pattern, according to the behavior during KSA. The colliding key pa...

The MacWilliams identity, which relates the weight distribution of a code to the weight distribution of its dual code, is useful in determining the weight distribution of codes. In this paper, we first provide an alternative proof to the MacWilliams identity for linear codes with the Hamming metric. An intermediate result of our approach is that the Hamming weight enumerator of the dual of any ...

Title of dissertation: BOUNDS ON THE SIZE OF CODES Punarbasu Purkayastha Doctor of Philosophy, 2010 Dissertation directed by: Professor Alexander Barg Department of Electrical and Computer Engineering and The Institute for Systems Research In this dissertation we determine new bounds and properties of codes in three different finite metric spaces, namely the ordered Hamming space, the binary Ha...

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 ...

Compressed sensing (CS) and 1-bit CS cannot directly recover quantized signals and require time consuming recovery. In this paper, we introduce Hamming compressed sensing (HCS) that directly recovers a k-bit quantized signal of dimensional n from its 1-bit measurements via invoking n times of Kullback-Leibler divergence based nearest neighbor search. Compared with CS and 1-bit CS, HCS allows th...

We show that there is a largely unexplored class of functions (positive polymatroids) that can define proper discrete metrics over pairs of binary vectors and that are fairly tractable to optimize over. By exploiting submodularity, we are able to give hardness results and approximation algorithms for optimizing over such metrics. Additionally, we demonstrate empirically the effectiveness of the...

Let x, y be strings of equal length. The Hamming distance h(x, y) between x and y is the number of positions in which x and y differ. If x is a cyclic shift of y, we say x and y are conjugates. We consider f(x, y), the Hamming distance between the conjugates xy and yx. Over a binary alphabet f(x, y) is always even, and must satisfy a further technical condition. By contrast, over an alphabet of...