相关论文: Adaptive Codes: A New Class of Non-standard Variab…

We consider universal variable-to-fixed length compression of memoryless sources with a fidelity criterion. We design a dictionary codebook over the reproduction alphabet which is used to parse the source stream. Once a source subsequence…

Linear codes have been an interesting subject of study for many years, as linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, a class of…

A novel adaptive binary decoding algorithm for LDPC codes is proposed, which reduces the decoding complexity while having a comparable or even better performance than corresponding non-adaptive alternatives. In each iteration the variable…

We introduce a new family of codes, termed weighted superimposed codes (WSCs). This family generalizes the class of Euclidean superimposed codes (ESCs), used in multiuser identification systems. WSCs allow for discriminating all bounded,…

Cyclic codes are an interesting type of linear codes and have applications in communication and storage systems due to their efficient encoding and decoding algorithms. They have been studied for decades and a lot of progress has been made.…

Cyclic codes and their various generalizations, such as quasi-twisted (QT) codes, have a special place in algebraic coding theory. Among other things, many of the best-known or optimal codes have been obtained from these classes. In this…

One of the most important and challenging problems in coding theory is to determine the optimal values of the parameters of a linear code and to explicitly construct codes with optimal parameters, or as close to the optimal values as…

We discuss inequalities holding between the vocabulary size, i.e., the number of distinct nonterminal symbols in a grammar-based compression for a string, and the excess length of the respective universal code, i.e., the code-based analog…

Neural codes are collections of binary strings motivated by patterns of neural activity. In this paper, we study algorithmic and enumerative aspects of convex neural codes in dimension 1 (i.e. on a line or a circle). We use the theory of…

Zipper codes are a framework for describing spatially-coupled product-like codes. Many well-known codes, such as staircase codes and braided block codes, are subsumed into this framework. New types of codes such as tiled diagonal and…

This paper presents prefix codes which minimize various criteria constructed as a convex combination of maximum codeword length and average codeword length or maximum redundancy and average redundancy, including a convex combination of the…

This paper introduces a new combinatorial construction for q-ary constant-weight codes which yields several families of optimal codes and asymptotically optimal codes. The construction reveals intimate connection between q-ary…

In addition to their applications in data storage, communications systems, and consumer electronics, LCD codes -- a class of linear codes -- have been employed in cryptography recently. LCD cyclic codes were referred to as reversible cyclic…

A code is called transitive if its automorphism group (the isometry group) of the code acts transitively on its codewords. If there is a subgroup of the automorphism group acting regularly on the code, the code is called propelinear. Using…

We introduce Reed-Solomon-Gabidulin codes which is, at the same time, an extension to Reed-Solomon codes on the one hand and Gabidulin codes on the other hand. We prove that our codes have good properties with respect to the minimal…

We provide new families of minimal codes in any characteristic. Also, an inductive construction of minimal codes is presented.

We define multi-block interleaved codes as codes that allow reading information from either a small sub-block or from a larger full block. The former offers faster access, while the latter provides better reliability. We specify the…

Batch codes are a useful notion of locality for error correcting codes, originally introduced in the context of distributed storage and cryptography. Many constructions of batch codes have been given, but few lower bound (limitation)…

Bounds on linear codes play a central role in coding theory, as they capture the fundamental trade-off between error-correction capability (minimum distance) and information rate (dimension relative to length). Classical results…

One-class anomaly detection aims to detect objects that do not belong to a predefined normal class. In practice training data lack those anomalous samples; hence state-of-the-art methods are trained to discriminate between normal and…