Array codes are intended to correct bursts of errors in communication through noisy channels. As in regular codes there is a notion of maximum distance separating (MDS) array codes. A so-called Perfect One-Factorization ...

Se hará una introducción a la teoría de códigos convolucionales y a continuación describiremos la construcción de códigos convolucionales como códigos de valoración en una familia uniparamétrica de curvas algebraicas. Los ...

In this paper, constructions of frameproof codes, separable codes, and B2 codes are obtained. For each family of codes, the Lovász Local Lemmais used to establish lower bounds for the codes. The obtained bounds match all ...

We prove that the cyclic and constacyclic codes constructed by Grassl and Rötteler in International Symposium on Information Theory (ISIT), pp. 1104–1108 (2015) are generalised Reed–Solomon codes. This note can be considered ...

In this work, two types of codes such that they both dominate and locate the vertices of a graph are studied. Those codes might be sets of detectors in a network or processors controlling a system whose set of responses ...

The focus of this bachelor thesis are maximum distance separable codes. A code is used to communicate over noise channel so any interferences that may occur can be detected and corrected. Maximum distance separable codes ...

Let $ C $ be a $ (n,q^{2k},n-k+1)_{q^2} $ additive MDS code which is linear over $ {\mathbb F}_q $. We prove that if $ n \geq q+k $ and $ k+1 $ of the projections of $ C $ are linear over $ {\mathbb F}_{q^2} $ then $ C $ ...

We introduce non-binary IPP set systems with traceability properties that have IPP codes and binary IPP set systems with traceability capabilities as particular cases. We prove an analogue of the Gilbert–Varshamov bound ...

In the next upcoming mobile generation era (5G), the demands for high-data-rate transmissions is predicted to grow considerably. Among new studies focused on how to support such demands, Random Linear Network Coding (RLNC) ...