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Cyclic codes are an interesting subclass of linear codes and have been used in consumer electronics, data transmission technologies, broadcast systems, and computer applications due to their efficient encoding and decoding algorithms. In…
Exceptional sequences are fundamental to investigate the derived categories of finite dimensional algebras. The aim of this note is to classify all the complete exceptional sequences over the path algebra of a Dynkin quiver of type $A_n$ in…
There are two variants of superposition coding schemes. Cover's original superposition coding scheme has code clouds of the identical shape, while Bergmans's superposition coding scheme has code clouds of independently generated shapes.…
This paper introduces a new family of reconstruction codes which is motivated by applications in DNA data storage and sequencing. In such applications, DNA strands are sequenced by reading some subset of their substrings. While previous…
We analyze a new group testing scheme, termed semi-quantitative group testing, which may be viewed as a concatenation of an adder channel and a discrete quantizer. Our focus is on non-uniform quantizers with arbitrary thresholds. For the…
We introduce a binary embedding framework, called Proximity Preserving Code (PPC), which learns similarity and dissimilarity between data points to create a compact and affinity-preserving binary code. This code can be used to apply fast…
Constrained sequence codes have been widely used in modern communication and data storage systems. Sequences encoded with constrained sequence codes satisfy constraints imposed by the physical channel, hence enabling efficient and reliable…
We consider a wireless sensors network scenario where two nodes detect correlated sources and deliver them to a central collector via a wireless link. Differently from the Slepian-Wolf approach to distributed source coding, in the proposed…
Noncrossing arc diagrams are combinatorial models for the equivalence classes of the lattice congruences of the weak order on permutations. In this paper, we provide a general method to endow these objects with Hopf algebra structures.…
We give recurrence relations for the enumeration of symmetric elements within four classes of arc diagrams corresponding to certain involutions and set partitions whose blocks contain no consecutive integers. These arc diagrams are…
A new approach to joint source-channel coding is presented in the context of communicating correlated sources over multiple access channels. Similar to the separation architecture, the joint source-channel coding system architecture in this…
Sequence decoding is one of the core components of most visual-lingual models. However, typical neural decoders when faced with decoding multiple, possibly correlated, sequences of tokens resort to simple independent decoding schemes. In…
We introduce a notion of harmonic chain for chain complexes over fields of positive characteristic. A list of conditions for when a Hodge decomposition theorem holds in this setting is given and we apply this theory to finite CW complexes.…
We construct new families of completely regular codes by concatenation methods. By combining parity check matrices of cyclic Hamming codes, we obtain families of completely regular codes. In all cases, we compute the intersection array of…
We generalize the notion of a de Bruijn sequence to a "multi de Bruijn sequence": a cyclic or linear sequence that contains every k-mer over an alphabet of size q exactly m times. For example, over the binary alphabet {0,1}, the cyclic…
The use of skew polynomial rings allows to endow linear codes with cyclic structures which are not cyclic in the classical (commutative) sense. Whenever these skew cyclic structures are carefully chosen, some control over the Hamming…
An alternating colouring function is defined on strings over the alphabet $\{0, 1\}$. It divides the strings in colourable and non-colourable ones. The points in the subshift of finite type defined by forbidding all non-colourable strings…
A class of linear block codes which simultaneously generalizes Gabidulin codes and a class of skew cyclic codes is defined. For these codes, both a Hartmann-Tzeng-like bound and a Roos-like bound, with respect to their rank distance, are…
We consider recursive decoding techniques for RM codes, their subcodes, and newly designed codes. For moderate lengths up to 512, we obtain near-optimum decoding with feasible complexity.
Single sequences like Legendre have high linear complexity. Known CDMA families of sequences all have low complexities. We present a new method of constructing CDMA sequence sets with the complexity of the Legendre from new frequency hop…