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This paper continues the series of papers that develop a new approach to syntax and semantics of dependent type theories. Here we study the interpretation of the rules of the identity types in the intensional Martin-Lof type theories on the…
Let $\mathbb{Z}_p$ be the ring of integers modulo a prime number $p$ where $p-1$ is a quadratic residue modulo $p$. This paper presents the study of constacyclic codes over chain rings $\mathcal{R}=\frac{\mathbb{Z}_p[u]}{\langle…
We present a novel approach, which is based on multiple-valued logic (MVL), to the verification and analysis of digital hardware designs, which extends the common ternary or quaternary approaches for simulations. The simulations which are…
A compound determinant identity for minors of rectangular matrices is established. As an application, we derive Vandermonde type determinant formulae for classical group characters.
In this article we consider linear codes coming from skew-symmetric determinantal varieties, which are defined by the vanishing of minors of a certain fixed size in the space of skew-symmetric matrices. In odd characteristic, the minimum…
The excellent performance of convolutional low-density parity-check codes is the result of the spatial coupling of individual underlying codes across a window of growing size, but much smaller than the length of the individual codes.…
Wilson lines are key objects in many QCD calculations. They are parallel transporters of the gauge field that can be used to render non-local operator products gauge invariant, which is especially useful for calculations concerning…
MDS self-dual codes over finite fields have attracted a lot of attention in recent years by their theoretical interests in coding theory and applications in cryptography and combinatorics. In this paper we present a series of MDS self-dual…
A classical method of constructing a linear code over $\gf(q)$ with a $t$-design is to use the incidence matrix of the $t$-design as a generator matrix over $\gf(q)$ of the code. This approach has been extensively investigated in the…
The compatibility of the semiclassical quantization of area-preserving maps with some exact identities which follow from the unitarity of the quantum evolution operator is discussed. The quantum identities involve relations between traces…
Linear codes with complementary-duals (LCD) are linear codes that intersect with their dual trivially. Multinegacirculant codes of index $2$ that are LCD are characterized algebraically and some good codes are found in this family. Exact…
Many tasks in computer vision can be cast as a "label changing" problem, where the goal is to make a semantic change to the appearance of an image or some subject in an image in order to alter the class membership. Although successful…
We describe a construction of generalized Maxwell theories -- higher analogues of abelian gauge theories -- in the factorization algebra formalism of Costello and Gwilliam, allowing for analysis of the structure of local observables. We…
We explore boundedness properties in the context of metric measure spaces, of some natural operators of convolution type whose study is suggested by certain transformations used in computer vision.
An efficient algorithm for classification of binary self-dual codes is presented. As an application, a complete classification of the self-dual codes of length 38 is given.
Using a probabilistic approach, we derive some interesting combinatorial identities involving gamma and beta functions. These results generalize certain well-known combinatorial identities involving binomial coefficients and special…
Menon's proof of the preservation of log-concavity of sequences under convolution becomes simpler when adapted to 2-sided infinite sequences. Under assumption of log-concavity of two 2-sided infinite sequences, the existence of the…
Adaptive (variable-length) codes associate variable-length codewords to symbols being encoded depending on the previous symbols in the input data string. This class of codes has been presented in [Dragos Trinca, cs.DS/0505007] as a new…
This work introduces a decoding strategy for binary self-dual codes possessing an automorphism of a specific type. The proposed algorithm is a hard decision iterative decoding scheme. The enclosed experiments show that the new decoding…
We present a new method for the derivation of convolution identities for finite sums of products of Bernoulli numbers. Our approach is motivated by the role of these identities in quantum field theory and string theory. We first show that…