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In the problem of blind reconstruction of channel codes, the receiver does not have the knowledge of the channel code used at the transmitter and the aim is to identify this unknown channel code corresponding to the given received sequence.…
This paper deals with a universal coding problem for a certain kind of multiterminal source coding system that we call the complementary delivery coding system. In this system, messages from two correlated sources are jointly encoded, and…
Recently, network coding technique has emerged as a promising approach that supports reliable transmission over wireless loss channels. In existing protocols where users have no interest in considering the encoded packets they had in coding…
A new family of codes, called clustering-correcting codes, is presented in this paper. This family of codes is motivated by the special structure of data that is stored in DNA-based storage systems. The data stored in these systems has the…
This paper presents encoding and decoding algorithms for several families of optimal rank metric codes whose codes are in restricted forms of symmetric, alternating and Hermitian matrices. First, we show the evaluation encoding is the right…
Cyclic codes are a subclass of linear codes and have wide applications in consumer electronics, data storage systems, and communication systems due to their efficient encoding and decoding algorithms. Cyclic codes with many zeros and their…
Determining the weight distribution of a linear code is a classical and fundamental topic in coding theory that has been extensively investigated. Repeated-root cyclic codes, which form a significant subclass of error-correcting codes, have…
An important family of codes for data storage systems, cryptography, consumer electronics, and network coding for error control in digital communications are the so-called cyclic codes. This kind of linear codes are also important due to…
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…
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…
Because of efficient encoding and decoding algorithms, cyclic codes are an important family of linear block codes, and have applications in communica- tion and storage systems. However, their weight distributions are known only for a few…
This paper discusses a stylized communications problem where one wishes to transmit a real-valued signal x in R^n (a block of n pieces of information) to a remote receiver. We ask whether it is possible to transmit this information reliably…
Subspace codes have important applications in random network coding. It is interesting to construct subspace codes with both sizes, and the minimum distances are as large as possible. In particular, cyclic constant dimension subspaces codes…
Irreducible cyclic codes are one of the largest known classes of block codes which have been investigated for a long time. However, their weight distributions are known only for a few cases. In this paper, a class of irreducible cyclic…
We adress the problem of the algebraic decoding of any cyclic code up to the true minimum distance. For this, we use the classical formulation of the problem, which is to find the error locator polynomial in terms of the syndroms of the…
The distance profiles of linear block codes can be employed to design variational coding scheme for encoding message with variational length and getting lower decoding error probability by large minimum Hamming distance. %, e.g. the design…
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, monomials and trinomials over…
We give a complete list of orbit codes that are generated by an irreducible cyclic group, i.e. an irreducible group having one generator. We derive some of the basic properties of these codes such as the cardinality and the minimum…
We generalize the notion of cyclic codes by using generator polynomials in (non commutative) skew polynomial rings. Since skew polynomial rings are left and right euclidean, the obtained codes share most properties of cyclic codes. Since…
In this letter, we propose a novel LDPC coding scheme to transmit extra bits aided by rotated signal constellations without any additional cost in transmission power or bandwidth. In the proposed scheme, the LDPC coded data are modulated by…