Lattices have been used in several problems in coding theory and cryptography. In this paper we approach q-ary lattices obtained via Constructions D, D′ and D. It is shown connections between Constructions D and D′. Bounds for the minimum l1-distance of lattices ΛD, ΛD′ and ΛD and, under certain conditions, a generator matrix for ΛD′ are presented. In addition, when the chain of codes used is c...

For a skip-free Markov process on Z + with generator matrix Q, we evaluate the joint Laplace transform of the occupation times before hitting the state n (starting at 0). This Laplace transform has a very straightforward and familiar expression. We investigate the properties of this Laplace transform, especially the conditions under which the occupation times form a Markov chain.

Locating the sources of forced low-frequency oscillations in power systems is an important problem. A number of proposed methods demonstrate their practical usefulness, but all of them rely on strong modeling assumptions and provide poor performance in certain cases for reasons still not well understood. This paper proposes a systematic method for locating the source of a forced oscillation by ...

We present a new shorter and simplified proof for the undecidability of the mortality problem in matrix semigroups, originally proved by Paterson in 1970. We use the clever coding technique introduced by Paterson to achieve also a new result, the undecidability of the vanishing (left) upper corner. Since our proof for the undecidability of the mortality problem uses only 8 matrices, a new bound...

We investigate the performance of regular systematic low-density generator matrix (LDGM) codes under the majority rule based (MB) iterative decoding algorithm. We derive a recursive form which can be used to extract the error performance of the code. Based on the recursive expression, we derive a tight non-recursive lower bound. These results can serve as efficient tools to evaluate the perform...

For an [n, k, d]3 code C with gcd(d, 3) = 1, we define a map wG from Σ = PG(k − 1, 3) to the set of weights of codewords of C through a generator matrix G. A t-flat Π in Σ is called an (i, j)t flat if (i, j) = (|Π ∩ F0|, |Π ∩ F1|), where F0 = {P ∈ Σ | wG(P ) ≡ 0 (mod 3)}, F1 = {P ∈ Σ | wG(P ) 6≡ 0, d (mod 3)}. We give geometric characterizations of (i, j)t flats, which involve quadrics. As an a...

We apply the well-known operator of sequences, the derivative D, on codewords of linear codes. The depth of a codeword c is the smallest integer i such that Dc (the derivative applied i consecutive times) is zero. We show that the depth distribution of the nonzero codewords of an [n; k] linear code consists of exactly k nonzero values, and its generator matrix can be constructed from any k nonz...

We investigate properties of two-weight codes over finite Frobenius rings, giving constructions for the modular case. A δ-modular code [15] is characterized as having a generator matrix where each column g appears with multiplicity δ|gR×| for some δ ∈ Q. Generalizing [10] and [5], we show that the additive group of a two-weight code satisfying certain constraint equations (and in particular a m...

In this paper two fast algorithms that use orthogonal similarity transformations to convert a symmetric rationally generated Toeplitz matrix to tridiagonal form are developed, as a means of finding the eigenvalues of the matrix efficiently. The reduction algorithms achieve cost efficiency by exploiting the rank structure of the input Toeplitz matrix. The proposed algorithms differ in the choice...

In this paper we present a procedural content generator using Non-negative Matrix Factorisation (NMF). We use representative levels from five dissimilar content generators to train NMF models that learn patterns about the various components of the game. The constructed models are then used to automatically generate content that resembles the training data as well as to generate novel content th...