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Linear complementary pairs (LCPs) of codes have been studied since they were introduced in the context of discussing mitigation measures against possible hardware attacks to integrated circuits. In this situation, the security parameters…
This work is a survey on completely regular codes. Known properties, relations with other combinatorial structures and constructions are stated. The existence problem is also discussed and known results for some particular cases are…
Function-correcting codes with data protection simultaneously protect both the data and a function of the data at distinct error-correction levels. When the function receives strictly stronger protection than the data, such a code is called…
Golay complementary pair (GCP), first introduced by Golay in 1951, has been extensively studied and widely applied in communication systems. A $q$-ary GCP $\{\mathbf{A},\mathbf{B}\}$ consists of two $q$-ary complex sequences…
Linear complementary-dual (LCD for short) codes are linear codes that intersect with their duals trivially. LCD codes have been used in certain communication systems. It is recently found that LCD codes can be applied in cryptography. This…
Since Massey introduced linear complementary dual (LCD) codes in 1992 and Bhasin et al. later formalized linear complementary pairs (LCPs) of codes - structures with important cryptographic applications - these code families have attracted…
Recent developments of high-order CCM have been to extend existing formalism and codes to $s \ge \frac 12$ for both the ground and excited states, and independently to "generalised" expectation values for a wide range of one- and two-body…
The problem of three-user multiple-access channel (MAC) with noiseless feedback is investigated. A new coding strategy is presented. The coding scheme builds upon the natural extension of the Cover-Leung (CL) scheme; and uses quasi-linear…
Motivated by the problem of reducing the peak to average power ratio (PAPR) of transmitted signals, we consider a design of complementary set matrices whose column sequences satisfy a correlation constraint. The design algorithm recursively…
Codes constructed from connected spatially coupled low-density parity-check code (SC-LDPCC) chains are proposed and analyzed. It is demonstrated that connecting coupled chains results in improved iterative decoding performance. The…
Three-qubit gates can be constructed using combinations of single-qubit and two-qubit gates, making their independent realization unnecessary. However, direct implementation of three-qubit gates reduces the depth of quantum circuits,…
In this paper, we propose a construction of full-rank q-ary 1-perfect codes over finite fields. This construction is a generalization of the Etzion and Vardy construction of full-rank binary 1-perfect codes (1994). Properties of…
One objective of this paper is to propose a novel class of sequence pairs, called "Quasi-orthogonal Z-complementary pairs (QOZCPs)", each depicting Z-complementary property for their aperiodic auto-correlation sums and also have a zero…
Golay complementary matrices (GCM) have recently drawn considerable attentions owing to its potential applications in omnidirectional precoding. In this paper we generalize the GCM to multi-dimensional Golay complementary arrays (GCA) and…
Linear complementary dual (LCD) codes and linear complementary pairs (LCP) of codes have been proposed for new applications as countermeasures against side-channel attacks (SCA) and fault injection attacks (FIA) in the context of direct sum…
Based on good algebraic structures and practicabilities, generalized quasi-cyclic (GQC) codes play important role in coding theory. In this paper, we study some results on GQC codes over $\mathbb{Z}_4$ including the normalized generating…
An important question in the study of quasi-perfect codes is whether such codes can be constructed for all possible lengths $n$. In this paper, we address this question for specific values of $n$. First, we investigate the existence of…
A known Kronecker construction of completely regular codes has been investigated taking different alphabets in the component codes. This approach is also connected with lifting constructions of completely regular codes. We obtain several…
Golay sequences are well suited for the use as codewords in orthogonal frequency-division multiplexing (OFDM), since their peak-to-mean envelope power ratio (PMEPR) in q-ary phase-shift keying (PSK) modulation is at most 2. It is known that…
A perfect code in a graph is an independent set of the graph such that every vertex outside the set is adjacent to exactly one vertex in the set. A circulant graph is a Cayley graph of a cyclic group. In this paper we study perfect codes in…