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We address the problems of constructing quantum convolutional codes (QCCs) and of encoding them. The first construction is a CSS-type construction which allows us to find QCCs of rate 2/4. The second construction yields a quantum…
Neural decoders were introduced as a generalization of the classic Belief Propagation (BP) decoding algorithms, where the Trellis graph in the BP algorithm is viewed as a neural network, and the weights in the Trellis graph are optimized by…
In this paper we present novel algorithms for several multidimensional data processing problems. We consider problems related to the computation of restricted clusters and of the diameter of a set of points using a new distance function. We…
Product codes (PCs) protect a two-dimensional array of bits using short component codes. Assuming transmission over the binary symmetric channel, the decoding is commonly performed by iteratively applying bounded-distance decoding to the…
In this paper, several families of irreducible constacyclic codes over finite fields and their duals are studied. The weight distributions of these irreducible constacyclic codes and the parameters of their duals are settled. Several…
It is well known that quantum codes can be constructed by means of classical symplectic dual-containing codes. This paper considers a family of two-generator quasi-cyclic codes and derives sufficient conditions for these codes to be…
Locally repairable codes (LRCs) have emerged as an important coding scheme in distributed storage systems (DSSs) with relatively low repair cost by accessing fewer non-failure nodes. Theoretical bounds and optimal constructions of LRCs have…
Optimal partitioned cyclic difference packings (PCDPs) are shown to give rise to optimal frequency-hopping sequences and optimal comma-free codes. New constructions for PCDPs, based on almost difference sets and cyclic difference matrices,…
The decomposition of a quasi-abelian code into shorter linear codes over larger alphabets was given in (Jitman, Ling, (2015)), extending the analogous Chinese remainder decomposition of quasi-cyclic codes (Ling, Sol\'e, (2001)). We give a…
A new class of folded subspace codes for noncoherent network coding is presented. The codes can correct insertions and deletions beyond the unique decoding radius for any code rate $R\in[0,1]$. An efficient interpolation-based decoding…
Two generalizations of the Hartmann--Tzeng (HT) bound on the minimum distance of q-ary cyclic codes are proposed. The first one is proven by embedding the given cyclic code into a cyclic product code. Furthermore, we show that unique…
In this paper, we propose a class of linear codes and obtain their weight distribution. Some of these codes are almost optimal. Moreover, several classes of constant composition codes(CCCs) are constructed as subcodes of linear codes.
Quantum synchronizable codes are quantum error-correcting codes designed to correct the effects of both quantum noise and block synchronization errors. While it is known that quantum synchronizable codes can be constructed from cyclic codes…
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…
The aim of this paper is to determine the algebraic structure of multidimensional cyclic codes over a finite chain ring $\mathfrak{R}$. An algorithm to find the generator polynomials of $n$ dimensional ($n$D) cyclic codes of length…
Locally repairable codes (LRCs) are a class of codes designed for the local correction of erasures. They have received considerable attention in recent years due to their applications in distributed storage. Most existing results on LRCs do…
Quadratic residue codes have been one of the most important classes of algebraic codes. They have been generalized into duadic codes and quadratic double circulant codes. In this paper we introduce a new subclass of double circulant codes,…
We consider the distributed function computation problem in asymmetric communication scenarios, where the sink computes some deterministic function of the data split among N correlated informants. The distributed function computation…
In this work, we study cyclic codes that have generators as Fibonacci polynomials over finite fields. We show that these cyclic codes in most cases produce families of maximum distance separable and optimal codes with interesting…
Encoding quantum information in a quantum error correction (QEC) code offers protection against decoherence and enhances the fidelity of qubits and gate operations. One of the fundamental challenges of QEC is to construct codes with…