Up until now, we have seen bounds that tell us good codes should be possible but we didn’t know how to construct such codes explicitly. The binary Reed-Solomon code gave us good rate but poor distance. Intuitively, we should be able to concatenate it with an inner code that would “amplify” its distance. Enumerating and searching codes takes O(2) time, so we can’t just find one good inner code a...

These words come from the ancient king Solomon, famous for his wisdom....... and also for his many wives. Here he is urging us to “keep” something; to safeguard it, to value it, because it lies at the foundation of human well-being. It is not our medications or our laryngoscopes that Solomon wants us to protect. These are but tools in our hands to help us manage our medical tasks efficiently. N...

Under polynomial time reduction, the maximun likelihood decoding of a linear code is equivalent to computing the error distance of a received word. It is known that the decoding complexity of standard Reed-Solomon codes at certain radius is at least as hard as the discrete logarithm problem over certain large finite fields. This implies that computing the error distance is hard for standard Ree...

The astonishing performance of concatenated codes attracted many researchers and this has resulted in an explosive amount of literature since their introduction few years ago. As concatenation between codes did not actually arise from applying a pre-existing theory, most of their outstanding features remain to be explained. This paper gives some explanation of the concatenation between Reed Sol...

A list decoding for an error-correcting code is a decoding algorithm that generates a list of codewords within a Hamming distance from the received vector, where can be greater than the error-correction bound. In [18], a list-decoding procedure for Reed–Solomon codes [19] was generalized to algebraic–geometric codes. A recent work [8] gives improved list decodings for Reed–Solomon codes and alg...

Codes with traceability properties are used in schemes where the identification of users that illegally redistribute content is required. For any code with traceability properties, the Identifiable Parent Property (c-IPP) seems to be less restrictive than the Traceability (c-TA) property. In this paper, we show that for Reed-Solomon codes both properties are in many cases equivalent. More preci...

The vehicle routing problem with time windows is a hard combinatorial optimization problem which has received considerable attention in the last decades. This paper proposes a two-stage hybrid algorithm for this transportation problem. The algorithm rst minimizes the number of vehicles using simulated annealing. It then minimizes travel cost using a large neighborhood search which may relocate ...

Digital audio broadcasting (DAB) systems for the AM band are being developed to provide higher-quality radio broadcasts, broader coverage, and data services. Transmission is typically done by means of multistreaming with QAM/OFDM in the high bits/sec/Hz regime, in which Reed–Solomon codes, either alone or in concatenation with inner trellis coded modulation (TCM), are natural choices for error ...

The people of the Solomon Islands represent an Austronesian (AN)-speaking population's adaptation to a humid tropical environment and subsistence of tuberous crops. Genome-wide association studies (GWASs) of other populations (e.g. the Human Genome Diversity Project [HGDP]) have suggested the existence of genotypes adaptive to ecoregion, diet, and subsistence, and that those genotypes are also ...

We provide a type-independent construction of an explicit basis for the semi-invariant harmonic differential forms arbitrary pseudo-reflection group in characteristic zero. Equivalently, we completely describe structure χ-isotypic components corresponding super coinvariant algebras one commuting and anti-commuting set variables, all linear characters χ. In type A, verify specialization conjectu...