Related papers: On the combinatorics of circular codes
We present a complete theory of bicircular high-order-harmonic emission from N-fold rotationally symmetric molecules. Using a rotating frame of reference we predict the complete structure of the high-order-harmonic spectra for arbitrary…
Encoding data as a set of unordered strings is receiving great attention as it captures one of the basic features of DNA storage systems. However, the challenge of constructing optimal redundancy codes for this channel remained elusive. In…
The subject of this paper is the cycle structure of the random permutation $\sigma$ of $[N]$, which is the product of $k$ independent random cycles of maximal length $N$. We use the character-based Fourier transform to study the number of…
A generic construction of linear codes over finite fields has recently received a lot of attention, and many one-weight, two-weight and three-weight codes with good error correcting capability have been produced with this generic approach.…
In this paper we investigate the class of constacyclic codes, which is a natural generalization of the class of cyclic and negacyclic codes. This class of codes is interesting in the sense that it contains codes with good or even optimal…
An elementary combinatorial Tanner graph construction for a family of near-regular low density parity check codes achieving high girth is presented. The construction allows flexibility in the choice of design parameters like rate, average…
The focus of this thesis is the study and construction of covering arrays, relying on maximal period sequences and other tools from finite fields. A covering array of strength $t$, denoted $\mathrm{CA}(N; t, k,v)$, is an $N\times k$ array…
Cyclic codes are the most studied subclass of linear codes and widely used in data storage and communication systems. Many cyclic codes have optimal parameters or the best parameters known. They are divided into simple-root cyclic codes and…
The Exact Circular Pattern Matching (ECPM) problem consists of reporting every occurrence of a rotation of a pattern $P$ in a text $T$. In many real-world applications, specifically in computational biology, circular rotations are of…
Neural codes are collections of binary strings motivated by patterns of neural activity. In this paper, we study algorithmic and enumerative aspects of convex neural codes in dimension 1 (i.e. on a line or a circle). We use the theory of…
In this paper, we discuss DNA codes that are cyclic or quasi-cyclic over $\Z_{4}+\omega \Z_{4}$, where $\omega^{2}=2+2\omega$ along with methods to construct these with combinatorial constraints. We also generalize results obtained for the…
Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory. In this paper we survey results on locally-testable and locally-decodable…
The purpose of this article is the study of the symmetries in a circular and linear harmonic oscillator chains system, and consequently use them as a means to find the eigenvalues of these configurations. Furthermore, a hidden…
Cyclic codes are among the most important families of codes in coding theory for both theoretical and practical reasons. Despite their prominence and intensive research on cyclic codes for over a half century, there are still open problems…
In an interesting paper Professor Cunsheng Ding provided three constructions of cyclic codes of length being a product of two primes. Numerical data shows that many codes from these constructions are best cyclic codes of the same length and…
Subspace codes and particularly constant dimension codes have attracted much attention in recent years due to their applications in random network coding. As a particular subclass of subspace codes, cyclic subspace codes have additional…
Based on the theoretical neuroscience, G. Cotardo and A. Ravagnavi in \cite{CR} introduced a kind of asymmetric binary codes called combinatorial neural codes (CN codes for short), with a "matched metric" $\delta_{r}$ called asymmetric…
A combinatorial model of molecular conformational space that was previously developped (J. Gabarro-Arpa, Comp. Biol. and Chem. 27, (2003) 153-159), had the drawback that structures could not be properly embedded beacause it lacked explicit…
Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Inspired by the recent work on binary cyclic codes published in…
Reconstruction codes are generalizations of error-correcting codes that can correct errors by a given number of noisy reads. The study of such codes was initiated by Levenshtein in 2001 and developed recently due to applications in modern…