A method of constructing binary linear codes is presentedthat have a minimum Hamming distance of five. Some efficient newcodes are obtained. In particular, a (47,36,5) code is obtained that hassix more information bits than the best previously known code with 11check bits.In Section II, we propose a general formulation of paritycheck matrix for the desired code. We then ...

A conflict-avoiding code (CAC) C of length n with weight k is a family of binary sequences of length n and weight k satisfying ∑ 0≤t≤n−1 xitxj,t+s ≤ 1 for any distinct codewords xi = (xi0, xi1, . . . , xi,n−1) and xj = (xj0, xj1, . . . , xj,n−1) in C and for any integer s, where the subscripts are taken modulo n. A CAC with maximal code size for given n and k is said to be optimal. A CAC has be...

The purpose of this paper is to improve the upper bounds of the minimum distances of self-dual codes over F5 for lengths 22, 26, 28, 32 − 40. In particular, we prove that there is no [22, 11, 9] self-dual code over F5, whose existence was left open in 1982. We also show that both the Hamming weight enumerator and the Lee weight enumerator of a putative [24, 12, 10] self-dual code over F5 are un...

We consider the problem of optimal, data-dependent zerotree design for use in weighted universal zerotree codes for image compression. A weighted universal zerotree code (WUZC) is a data compression system that replaces the single, data-independent zerotree of Said and Pearlman with an optimal collection of zerotrees for good image coding performance across a wide variety of possible sources. W...

A (v, k, λa, λc) optical orthogonal code C is a family of (0, 1)-sequences of length v and weight k satisfying the following two correlation properties: (1) ∑ 0≤t≤v−1xtxt+i ≤ λa for any x = (x0, x1, . . . , xv−1) and any integer i 6≡ 0 mod v; and (2) ∑ 0≤t≤v−1xtyt+i ≤ λb for any x = (x0, x1, . . . , xv−1), y = (y0, y1, . . . , yv−1) with x 6= y, and any integer i, where subscripts are taken mod...

An n symbol source which has a Huffman code with codelength vector Ln = (1, 2, 3, · · · , n − 2, n − 1, n − 1) is called an anti-uniform source. In this paper, it is shown that for this class of sources, the optimal fix-free code and symmetric fix-free code is C∗ n = (0, 11, 101, 1001, · · · , 1 n−2 { }} { 0 · · · 0 1).

Binary code learning, a.k.a., hashing, has been recently popular due to its high efficiency in large-scale similarity search and recognition. It typically maps high-dimensional data points to binary codes, where data similarity can be efficiently computed via rapid Hamming distance. Most existing unsupervised hashing schemes pursue binary codes by reducing the quantization error from an origina...

In this thesis we address the problem of optimal code generation for irregular architectures such as Digital Signal Processors (DSPs). Code generation consists mainly of three interrelated optimization tasks: instruction selection (with resource allocation), instruction scheduling and register allocation. These tasks have been discovered to be NP-hard for most architectures and most situations....

Assume that G = (V,E) is an undirected graph, and C ⊆ V . For every v ∈ V , we denote by I(v) the set of all elements of C that are within distance one from v. If the sets I(v) \ {v} for v ∈ V are all nonempty, and, moreover, the sets {I(v), I(v) \ {v}} for v ∈ V are disjoint, then C is called a strongly identifying code. The smallest possible density of a strongly identifying code in the infin...