We prove that Welch Costas arrays are in general not symmetric and that there exist two special families of symmetric Golomb Costas arrays: one is the well-known Lempel family, while the other, although less well known, leads actually to the construction of dense Golomb rulers. © 2008 Elsevier B.V. All rights reserved.

A model of a quantum information source is proposed, based on the Gibbs ensemble of ideal (free) particles (bosons or fermions). We identify the (thermodynamic) von Neumann entropy as the information rate and establish the classical Lempel–Ziv universal coding algorithm in Grassberger’s form for such a source. This generalises the Schumacher theorem to the case of non-IID qubits.

Ziv-Lempel and Crochemore factorization are two kinds of factorizations of words related to text processing. In this paper, we find these factorizations for standard epiesturmian words. Thus the previously known c-factorization of standard Sturmian words is provided as a special case. Moreover, the two factorizations are compared.

The Lempel-Ziv-Welch (LZW) compression algorithm is widely used because it achieves an excellent compromise between compression performance and speed of execution. A simple way to improve the compression without significantly degrading its speed is proposed, and experimental data shows that it works in practice. Even better results are achieved with an additional optimization of “phasing in” bi...

In this paper, using the theory of polynomial residue class rings, a new construction is proposed for frequency hopping patterns having optimal Hamming autocorrelation with respect to the well-known Lempel-Greenberger bound. Based on the proposed construction, many new Peng-Fan optimal families of frequency hopping sequences are obtained. The parameters of these sets of frequency hopping sequen...

We derive recurrences for counting the number a(n, r) of sequences of length n with Lempel-Ziv complexity r, which has important applications, for instance testing randomness of binary sequences. We also give algorithms to compute these recurrences. We employed these algorithms to compute a(n, r) and expected value, EPn, of number of patterns of a sequence of length n, for relatively large n. W...

In this paper, for a prime p and a positive integer q such that q|pn − 1, we constructed q-ary Lempel– Cohn–Eastman(LCE) sequences with period p − 1. These sequences have maximum autocorrelation magnitude bounded by 4. Particularly, in the case of q = 3, the maximum autocorrelation magnitude of the ternary LCE sequences is 3. And the maximum autocorrelation magnitude of the quaternary LCE seque...

Given a text T [1..u] over an alphabet of size σ = O(polylog(u)) and with k-th order empirical entropy Hk(T ), we propose a new compressed full-text self-index based on the Lempel-Ziv (LZ) compression algorithm, which replaces T with a representation requiring about three times the size of the compressed text, i.e (3+ ǫ)uHk(T )+ o(u log σ) bits, for any ǫ > 0 and k = o(log σ u), and in addition...

The Lempel-Ziv parsing of a string (LZ77 for short) is one of the most important and widely-used algorithmic tools in data compression and string processing. We show that the LempelZiv parsing of a string of length n on an alphabet of size σ can be computed in O(n log log σ) time (O(n) time if we allow randomization) using O(n log σ) bits of working space; that is, using space proportional to t...