Related papers: On two variations of identifying codes
Linear codes with few weights have applications in consumer electronics, communication, data storage system, secret sharing, authentication codes, association schemes, and strongly regular graphs. This paper first generalizes the method of…
Decoding of convolutional codes poses a significant challenge for coding theory. Classical methods, based on e.g. Viterbi decoding, suffer from being computationally expensive and are restricted therefore to codes of small complexity. Based…
Linear Complementary Dual codes (LCD) are binary linear codes that meet their dual trivially. We construct LCD codes using orthogonal matrices, self-dual codes, combinatorial designs and Gray map from codes over the family of rings $R_k$.…
In this paper we study function-correcting codes, a new class of codes designed to protect the function evaluation of a message against errors. We show that FCCs are equivalent to irregular-distance codes, i.e., codes that obey some given…
The problem of finding code distance has been long studied for the generic ensembles of linear codes and led to several algorithms that substantially reduce exponential complexity of this task. However, no asymptotic complexity bounds are…
Low complexity error correction code is a key enabler for next generation ultra-reliable low-latency communications (xURLLC) in six generation (6G). Against this background, this paper proposes a decoding scheme for linear block code by…
Linear complementary dual (LCD) codes are linear codes which intersect their dual codes trivially, which have been of interest and extensively studied due to their practical applications in computational complexity and information…
Detecting similar code fragments, usually referred to as code clones, is an important task. In particular, code clone detection can have significant uses in the context of vulnerability discovery, refactoring and plagiarism detection.…
Linear codes and $t$-designs are interactive with each other. It is well known that some $t$-designs have been constructed by using certain linear codes in recent years. However, only a small number of infinite families of the extended…
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.…
In his Ph.D. disseration, Feldman and his collaborators define the linear programming decoder for binary linear codes, which is a linear programming relaxation of the maximum-likelihood decoding problem. This decoder does not, in general,…
In order to protect intellectual property against untrusted foundry, many logic-locking schemes have been developed. The main idea of logic locking is to insert a key-controlled block into a circuit to make the circuit function incorrectly…
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)…
Given a family of systems, identifying stabilizing switching signals in terms of infinite walks constructed by concatenating cycles on the underlying directed graph of a switched system that satisfy certain conditions, is a well-known…
License Plate Recognition Systems are used to determine the license plate number of a vehicle. The current system mainly uses Optical Character Recognition to recognize the number plate. There are several problems to this system. Some of…
Polar codes are linear block codes that can achieve channel capacity at infinite code length. Successive cancellation list (SCL) decoding relies on a set of parallel decoders; it yields good error-correction performance at finite code…
In data storage and data transmission, certain patterns are more likely to be subject to error when written (transmitted) onto the media. In magnetic recording systems with binary data and bipolar non-return-to-zero signaling, patterns that…
Two new constructions are presented for coils and snakes in the hypercube. Improvements are made on the best known results for snake-in-the-box coils of dimensions 9, 10 and 11, and for some other circuit codes of dimensions between 8 and…
Multiclass learning problems involve finding a definition for an unknown function f(x) whose range is a discrete set containing k > 2 values (i.e., k ``classes''). The definition is acquired by studying collections of training examples of…
We characterize the affine-invariant maximal extended cyclic codes. Then by the CSS construction, we derive from these codes a family of pure quantum codes. Also for ordnq even, a new family of degenerate quantum stabilizer codes is derived…