Related papers: A Class of Narrow-Sense BCH Codes
Minimal codes are a class of linear codes which gained interest in the last years, thanks to their connections to secret sharing schemes. In this paper we provide the weight distribution and the parameters of families of minimal codes…
In this paper, we mainly study quaternary linear codes and their binary subfield codes. First we obtain a general explicit relationship between quaternary linear codes and their binary subfield codes in terms of generator matrices and…
This paper computationally obtains optimal bounded-weight, binary, error-correcting codes for a variety of distance bounds and dimensions. We compare the sizes of our codes to the sizes of optimal constant-weight, binary, error-correcting…
The size reduction of transistors in the latest flash memory generation has resulted in programming and data erasure issues within these designs. Consequently, ensuring reliable data storage has become a significant challenge for these…
Cyclic codes are an important subclass of linear codes and have wide applications in data storage systems, communication systems and consumer electronics. In this paper, two families of optimal ternary cyclic codes are presented. The first…
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. Let $m=2\ell+1$ for an integer $\ell\geq 1$…
A new lower bound on the minimum distance of q-ary cyclic codes is proposed. This bound improves upon the Bose-Chaudhuri-Hocquenghem (BCH) bound and, for some codes, upon the Hartmann-Tzeng (HT) bound. Several Boston bounds are special…
Constant dimension codes, with a prescribed minimum distance, have found recently an application in network coding. All the codewords in such a code are subspaces of $\F_q^n$ with a given dimension. A computer search for large constant…
Cyclic codes have been widely used in digital communication systems and consume electronics as they have efficient encoding and decoding algorithms. The weight distribution of cyclic codes has been an important topic of study for many…
To equip DNA-based data storage with random-access capabilities, Yazdi et al. (2018) prepended DNA strands with specially chosen address sequences called primers and provided certain design criteria for these primers. We provide explicit…
Quantum computing is deemed to require error correction at scale to mitigate physical noise by reducing it to lower noise levels while operating on encoded logical qubits. Popular quantum error correction schemes include CSS code, of which…
Non-binary linear block codes (NB-LBCs) are an important class of error-correcting codes that are especially competent in correcting burst errors. They have broad applications in modern communications and storage systems. However, efficient…
We study $q$-ary codes with distance defined by a partial order of the coordinates of the codewords. Maximum Distance Separable (MDS) codes in the poset metric have been studied in a number of earlier works. We consider codes that are close…
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…
Linear codes with a few weights can be applied to communication, consumer electronics and data storage system. In addition, the weight hierarchy of linear codes has many applications such as on the type II wire-tap channel, dealing with…
After recalling the definition of codes as modules over skew polynomial rings, whose multiplication is defined by using an automorphism and a derivation, and some basic facts about them, in the first part of this paper we study some of…
Codes in finite projective spaces equipped with the subspace distance have been proposed for error control in random linear network coding. Here we collect the present knowledge on lower and upper bounds for binary subspace codes for…
Polycyclic codes offer a natural generalization of cyclic codes and provide a broader algebraic framework for constructing linear codes with good parameters. In this paper, we study binary polycyclic codes associated with powers of…
This paper proposes a quasi-belief propagation decoder for BCH codes that systematically integrates domain knowledge--specifically, channel noise variance, the cyclic property of the codes, and the deliberate redundancy in their…
The hull of a linear code over finite fields is the intersection of the code and its dual, and linear codes with small hulls have applications in computational complexity and information protection. Linear codes with the smallest hull are…