Related papers: Gold type codes of higher relative dimension
In this paper, classification of higher dimensional Kundt geometry is revisited as the dimension of the spacetime $D \rightarrow\infty$. In addition to previous studies, in order to Kundt geometry becomes algebraically special spacetime…
This correspondence introduces two new constructive techniques to complete the determination of the sizes of optimal q-ary codes of constant weight three and distance four.
We have examined the valence-band electronic structures of gold and silver in the same column in the periodic table with nominally filled d orbitals by means of a recently developed polarization-dependent hard x-ray photoemission. Contrary…
Linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, several classes of $p$-ary linear codes with two or three weights are constructed…
Coset constructions of $q$-ary Reed-Muller codes can be used to store secrets on a distributed storage system in such a way that only parties with access to a large part of the system can obtain information while still allowing for local…
EFRST20, the notion of $c$-differentials was introduced as a potential expansion of differential cryptanalysis against block ciphers utilizing substitution boxes. Drawing inspiration from the technique of higher order differential…
For a positive integer $b\ge2$, the $b$-symbol code is a new coding framework proposed to combat $b$-errors in $b$-symbol read channels. Especially, the $2$-symbol code is called a symbol-pair code. Remarkably, a classical maximum distance…
We give a new realization of arbitrary level perfect crystals and arbitrary level irreducible highest weight crystals of type $D_n^{(1)}$, in the language of Young walls. The notions of splitting of blocks and slices play crucial roles in…
A sharp upper bound for the maximum integer not belonging to an ideal of a numerical semigroup is given and the ideals attaining this bound are characterized. Then the result is used, through the so-called Feng-Rao numbers, to bound the…
We consider linear codes over a finite field of odd characteristic, derived from determinantal varieties, obtained from symmetric matrices of bounded ranks. A formula for the weight of a code word is derived. Using this formula, we have…
Polynomial remainder codes are a large class of codes derived from the Chinese remainder theorem that includes Reed-Solomon codes as a special case. In this paper, we revisit these codes and study them more carefully than in previous work.…
Some inequalities for different types of convexity are established.
In this survey we discuss some combinatorial aspects of higher cluster categories.
Recently, linear codes constructed from defining sets have been investigated extensively and they have many applications. In this paper, for an odd prime $p$, we propose a class of $p$-ary linear codes by choosing a proper defining set.…
We obtain new recurrence relations, an explicit formula, and convolution identities for higher order geometric polynomials. These relations generalize known results for geometric polynomials, and lead to congruences for higher order…
We study the problem of constructing good space-time codes for broadcasting $K$ independent messages over a MIMO network to $L$ users, where each user demands all the messages and already has a subset of messages as side information. As a…
In this paper we present a concrete algebraic construction of a novel class of convolutional codes. These codes are built upon generalized Vandermonde matrices and therefore can be seen as a natural extension of Reed-Solomon block codes to…
This paper introduces a new counting code. Its design was motivated by distributed video coding where, for decoding, error correction methods are applied to improve predictions. Those error corrections sometimes fail which results in…
We give an upper bound that relates the minimum weight of a nonzero componentwise product of codewords from some given number of linear codes, with the dimensions of these codes. Its shape is a direct generalization of the classical…
Cyclic codes are a subclass of linear codes and have wide applications in consumer electronics, data storage systems, and communication systems due to their efficient encoding and decoding algorithms. Cyclic codes with many zeros and their…