Related papers: Alternative Metrics
A new ensemble of structured codes is introduced. These codes are called Quasi Linear Codes (QLC). The QLC's are constructed by taking subsets of linear codes. They have a looser structure compared to linear codes and are not closed under…
Any program that is designed to accomplish certain objectives, needs to establish program level controls pertaining to the overall goal. A critical aspect that determines the success of a program is the quality of the controls and their…
Bi-modal (respectively, multi-modal) constrained coding refers to an encoding model whereby a user input block can be mapped to two (respectively, multiple) codewords. In current storage applications, such as optical disks, multi-modal…
Spread codes and orbit codes are special families of constant dimension subspace codes. These codes have been well-studied for their error correction capability and transmission rate, but the question of how to encode messages has not been…
In general, if there is one device A with the same performance as many devices B, it would be better to replace many devices with one device. In order to determine the number of devices that can be reduced, it is important to determine the…
Sectors at centre of affine quadrics with point symmetry are investigated over arbitrary fields of characteristic different from two. As an application we demonstrate nice formulas for the area and the volume of such planar and spatial…
The bit-wise unequal error protection problem, for the case when the number of groups of bits $\ell$ is fixed, is considered for variable length block codes with feedback. An encoding scheme based on fixed length block codes with erasures…
Extending the `metric spaces' of Lawvere, we study `real metrics', with values in the extended real line. Formally, this ordered set is a symmetric monoidal closed category, and our structures are enriched categories on the latter.…
The state-of-the-art error correcting codes are based on large random constructions (random graphs, random permutations, ...) and are decoded by linear-time iterative algorithms. Because of these features, they are remarkable examples of…
We propose the first non-trivial generic decoding algorithm for codes in the sum-rank metric. The new method combines ideas of well-known generic decoders in the Hamming and rank metric. For the same code parameters and number of errors,…
Weighted poset block metric is a generalization of weighted poset metric introduced by Panek et al. ([\ref{panek}]) and the metric for linear error-block codes introduced by Feng et al. ([\ref{FENG}]). This type of metrics includes many…
Subspace codes form the appropriate mathematical setting for investigating the Koetter-Kschischang model of fault-tolerant network coding. The Main Problem of Subspace Coding asks for the determination of a subspace code of maximum size…
Software measurement programs have emerged as compounds of several measurement activities that are pursued as part of a combined effort of several parties within a software organization, based on interests that the organization has…
A generalization of metric space is presented which is shown to admit a theory strongly related to that of ordinary metric spaces. To avoid the topological effects related to dropping any of the axioms of metric space, first a new, and…
Attack Trees (ATs) are a widely used tool for security analysis. ATs can be employed in quantitative security analysis through metrics, which assign a security value to an AT. Many different AT metrics exist, and there exist multiple…
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…
Looping is one of the fundamental logical instructions used for repeating a block of code. It is used in programs across all programming languages. Traditionally, in languages like C, the for loop is used extensively for repeated execution…
As a result of their applications in network coding, space-time coding, and coding for criss-cross errors, matrix codes have garnered significant attention; in various contexts, these codes have also been termed rank-metric codes,…
The main phases of applied statistical work are discussed in general terms. The account starts with the clarification of objectives and proceeds through study design, measurement and analysis to interpretation. An attempt is made to extract…
Alternative set theory (AST) may be suitable for the ones who try to capture objects or phenomenons with some kind of indefiniteness of a border. While AST provides various notions for advanced mathematical studies, correspondence of them…