Cyclic Low-Density MDS Array Codes

We construct two infinite families of low density MDS array codes which are also cyclic. One of these families includes the first such sub-family with redundancy parameter r > 2. The two constructions have different algebraic formulations, though they both have the same indirect structure. First MDS codes that are not cyclic are constructed and then by applying a certain mapping to their parity check matrices, non-equivalent cyclic codes with the same distance and density properties are obtained. Using the same proof techniques, a third infinite family of quasi-cyclic codes can be constructed

Cyclic distance-preserving codes on a constant-weight basis

AbstractAn approach to constructing cyclic distance-preserving codes based on the choice of an approaching basis of a linear code with distance 2 is discussed

Decoding of Convolutional Codes over the Erasure Channel

In this paper we study the decoding capabilities of convolutional codes over the erasure channel. Of special interest will be maximum distance profile (MDP) convolutional codes. These are codes which have a maximum possible column distance increase. We show how this strong minimum distance condition of MDP convolutional codes help us to solve error situations that maximum distance separable (MDS) block codes fail to solve. Towards this goal, we define two subclasses of MDP codes: reverse-MDP convolutional codes and complete-MDP convolutional codes. Reverse-MDP codes have the capability to recover a maximum number of erasures using an algorithm which runs backward in time. Complete-MDP convolutional codes are both MDP and reverse-MDP codes. They are capable to recover the state of the decoder under the mildest condition. We show that complete-MDP convolutional codes perform in certain sense better than MDS block codes of the same rate over the erasure channel.Comment: 18 pages, 3 figures, to appear on IEEE Transactions on Information Theor

Convolutional and tail-biting quantum error-correcting codes

Rate-(n-2)/n unrestricted and CSS-type quantum convolutional codes with up to 4096 states and minimum distances up to 10 are constructed as stabilizer codes from classical self-orthogonal rate-1/n F_4-linear and binary linear convolutional codes, respectively. These codes generally have higher rate and less decoding complexity than comparable quantum block codes or previous quantum convolutional codes. Rate-(n-2)/n block stabilizer codes with the same rate and error-correction capability and essentially the same decoding algorithms are derived from these convolutional codes via tail-biting.Comment: 30 pages. Submitted to IEEE Transactions on Information Theory. Minor revisions after first round of review

The Road From Classical to Quantum Codes: A Hashing Bound Approaching Design Procedure

Powerful Quantum Error Correction Codes (QECCs) are required for stabilizing and protecting fragile qubits against the undesirable effects of quantum decoherence. Similar to classical codes, hashing bound approaching QECCs may be designed by exploiting a concatenated code structure, which invokes iterative decoding. Therefore, in this paper we provide an extensive step-by-step tutorial for designing EXtrinsic Information Transfer (EXIT) chart aided concatenated quantum codes based on the underlying quantum-to-classical isomorphism. These design lessons are then exemplified in the context of our proposed Quantum Irregular Convolutional Code (QIRCC), which constitutes the outer component of a concatenated quantum code. The proposed QIRCC can be dynamically adapted to match any given inner code using EXIT charts, hence achieving a performance close to the hashing bound. It is demonstrated that our QIRCC-based optimized design is capable of operating within 0.4 dB of the noise limit

Constacyclic and Linear Complementary Dual Codes Over Fq + uFq

This article discusses linear complementary dual (LCD) codes over ℜ = Fq+uFq(u2=1) where q is a power of an odd prime p. Authors come up with a new Gray map from ℜn to F2nq and define a new class of codes obtained as the gray image of constacyclic codes over .ℜ Further, we extend the study over Euclidean and Hermitian LCD codes and establish a relation between reversible cyclic codes and Euclidean LCD cyclic codes over ℜ. Finally, an application of LCD codes in multisecret sharing scheme is given

ADVANCED MODELLING OF OVER-STROKE DISPLACEMENT CAPACITY FOR CURVED SURFACE SLIDER DEVICES

This doctoral dissertation aims to report on the research work carried out and to provide a contribution to the field of seismic base isolation. Since its introduction, the base isolation strategy proved to be an effective solution for the protection of structures and their components from the earthquake-induced damage, enhancing their resilience and implying a significative decrease in time and cost of repair compared to a conventional fixed-base structure. Sliding isolation devices feature some important characteristics, over other devices, that make them particularly suitable for the application in the existing buildings retrofit such as the high displacements capacity combined with limited plan dimensions. Even though these devices diffusion has gotten more popular worldwide in last years, a full understanding of their performances and limits as well as their behaviour under real seismic excitations has not been yet completely achieved. When Curved Surface Sliders reach their displacement capacity, they enter the so-called over-stroke sliding regime which is characterized by an increase in stiffness and friction coefficient. While in the over-stroke displacements regime, anyways, sliding isolators are still capable, until certain threshold values, of preserving their ability to support gravity loads. In this doctoral dissertation, the analysis of Curved Surface Sliding devices influence on different structures and under different configurations is presented and a tool for to help professionals in the design phase is provided. The research main focuses are: i) the numerical investigation of the over-stroke displacement influence on base isolated structures; ii) the numerical investigation of displacement retaining elements influence on base isolated structures; iii) the development of a mechanical model and an algebraic solution describing the over-stroke sliding regime and the associated limit displacements