Inspired by engineering of high-speed switching with quality of service, this paper introduces a new approach to classify finite lattices by the concept of cut-through coding. An n-ary cut-through code of a finite lattice encodes all lattice elements by distinct n-ary strings of a uniform length such that for all j, the initial j encoding symbols of any two elements x and y determine the initia...

In this paper, given a composite integer n, we propose a method of constructing p-ary low correlation zone(LCZ) sequences of period p − 1 from p-ary m-sequences of the same length. The new construction method is a generalized form of the quaternary LCZ sequence by Kim, Jang, No, and Chung in the view of the alphabet size. The correlation distribution of these new p-ary LCZ sequences is derived.

In this paper, the cross-correlation distribution between a p-ary m-sequence s(t) and its p + 1 distinct decimated sequences s(dt + l) is derived. For an odd prime p, an even integer n, and d = pk + 1 with gcd(n, k) = 1, there are p + 1 distinct decimated sequences s(dt + l), 0 ≤ l < p + 1, for a p-ary m-sequence s(t) of period pn − 1 because gcd(d, pn − 1) = p + 1. The maximum magnitude of the...

This paper presents three simple and efficient algorithms for generating, ranking and unranking t-ary trees in a lexicographic order. The simplest idea of encoding a t-ary tree with n nodes as a bit-string of length t*n is exploited to its full advantages. It is proved that the lexicographic order in the set of t-ary trees with n nodes is preserved in the set of bit-strings of length t*n, using...

In this paper, for an odd prime p, two positive integers n, m with n = 2m, and pm ≡ 1 (mod 4), we derive an upper bound on the magnitude of the cross-correlation function between two decimated sequences of a p-ary m-sequence. The two decimation factors are 2 and 2(pm + 1), and the upper bound is derived as 3 2 p m + 2 . In fact, those two sequences correspond to the p-ary sequences used for the...