This study investigated saccadic behaviour during the fusional vergence test as a function of disparity vergence demand. Participants’ divergence and convergence fusional vergence ranges were measured in an haploscopic setup. Disparity of a column of letters increased to 45 prism dioptres (PD) at 1 PD/s for both divergence and convergence. Eye movements were recorded using an Eyelink 1000 Plus, and a velocity-threshold-based algorithm was used to detect saccades. Saccades followed the main sequence, and their characteristics varied significantly with the direction of the underlying vergence movement. Saccades’ amplitude while fusion was maintained was smaller than during diplopia. Participants experienced diplopia for a longer time during divergence evaluation, which resulted in a higher prevalence of horizontal saccades than during convergence. This study highlights the impact of binocular conditions on saccade characteristics during fusional vergence tests, thus contributing to the understanding of how the visual system adapts to different vergence demands.

In a realistic distributed storage environment, like the ones used in companies dedicated to the task of storing information over a network, storage nodes are usually placed in racks, a metallic support designed to accommodate electronic equipment. It is known that the communication (bandwidth) cost between nodes which are in the same rack is much lower than between nodes which are in different racks. In this paper, a new mathematical model for a distributed storage environment where the storage nodes are placed in two racks is presented and analyzed.

In the traditional two-rack distributed storage system (DSS) model, due to the assumption that the storage capacity of each node is the same, the minimum bandwidth regenerating (MBR) point becomes infeasible. In this paper, we design a new non-homogeneous two-rack model by proposing a generalization of the threshold function used to compute the tradeoff curve. We prove that by having the nodes in the rack with higher regenerating bandwidth stores more information, all the points on the tradeoff curve, including the MBR point, become feasible. Finally, we show how the non-homogeneous two-rack model outperforms the traditional model in the tradeoff curve between the storage per node and the repair bandwidth.

Nowadays, it is possible to optimize the storage size of large files in distributed environments, maintaining the same availability level in the system. Although replication (backups) is the most used option, it is possible to make use of erasure coding in order to significantly compress the storage size [1]. However, using erasure coding, more information needs to be transmitted than when using replication, in order to replace a node which has failed. This is called the code repair problem. The amount of transmitted information can be an important issue when the file size is very large. If network coding is used in conjunction with erasure codes, the transmitted information can be reduced by compressing the sent data in the regeneration phase. This solution minimizes the code repair problem and consists of the use of regenerating codes introduced by Dimakis et al. [2]. Nevertheless, using network coding, computational resources for any node in the system are required, since linear operations must be carried out and systems of equations must be solved in the nodes. This requirement is too strong for many simple storage devices [3]. In this paper a new family of Minimum Storage Regenerating codes is proposed. These codes not only compress the storage size using erasure coding and achieve optimality for the amount of transmitted information when d = k + 1, but also demand few computational requirements. Therefore, they could be used for simple hard discs without computational resources.

Recently, new families of quaternary linear Reed–Muller codes have been introduced. They satisfy that, after the Gray map, the corresponding${\BBZ}_{4}$-linear codes have the same parameters and properties as the codes of the binary linear Reed–Muller family. A structural invariant, the dimension of the kernel, for binary codes is used to classify completely these${\BBZ}_{4}$-linear codes. The dimension of the kernel for these${\BBZ}_{4}$-linear codes is established generalizing the known results about the dimension of the kernel for${\BBZ}_{4}$-linear Hadamard and${\BBZ}_{4}$-linear extended 1-perfect codes.

In this paper, new quaternary Plotkin constructions are given and are used to obtain new families of quaternary codes. The parameters of the obtained codes, such as the length, the dimension, and the minimum distance, are studied. Using these constructions, new families of quaternary Reed-Muller (RM) codes are built with the peculiarity that after using the Gray map the obtained Z4-linear codes have the same parameters and fundamental properties as the codes in the usual binary linear RM family. To make the duality relationships in the constructed families more evident, the concept of Kronecker inner product is introduced.

A class of binary group codes is investigated. These codes are the propelinear codes, defined over the Hamming metric space F/sup m/, F=(0, 1), with a group structure. Generally, they are neither Abelian nor translation-invariant codes but they have good algebraic and combinatorial properties. Linear codes and Z/sub 4/-linear codes can be seen as a subclass of propelinear codes. It is shown here that the subclass of translation-invariant propelinear codes is of type Z/sub 2//sup k1//spl oplus/Z/sub 4//sup k2//spl oplus/Q/sub 8/(k3) where Q/sub 8/ is the non-Abelian quaternion group of eight elements. Exactly, every translation-invariant propelinear code of length n can be seen as a subgroup of Z/sub 2//sup k1//spl oplus/Z/sub 4//sup k2//spl oplus/Q/sub 8//sup k3/ with k/sub 1/+2k/sub 2/+4k/sub 3/=n. For k/sub 2/=k/sub 3/=0 we obtain linear binary codes and for k/sub 1/=k/sub 3/=0 we obtain Z/sub 4/-linear codes. The class of additive propelinear codes-the Abelian subclass of the translation-invariant propelinear codes-is studied and a family of nonlinear binary perfect codes with a very simply construction and a very simply decoding algorithm is presented.