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A general lossless joint source-channel coding (JSCC) scheme based on linear codes and random interleavers for multiple-access channels (MACs) is presented and then analyzed in this paper. By the information-spectrum approach and the…

Information Theory · Computer Science 2009-03-31 Shengtian Yang , Yan Chen , Peiliang Qiu

Linear codes can be employed to construct authentication codes, which is an interesting area of cryptography. The parameters of the authentication codes depend on the complete weight enumerator of the underlying linear codes. In order to…

Information Theory · Computer Science 2015-05-27 Can Xiang , Hao Liu

Combinatorial $t$-designs have wide applications in coding theory, cryptography, communications and statistics. It is well known that the supports of all codewords with a fixed weight in a code may give a $t$-design. In this paper, we first…

Combinatorics · Mathematics 2019-04-10 Xiaoni Du , Rong Wang , Cuiling Fan

We consider linear cyclic codes with the locality property, or locally recoverable codes (LRC codes). A family of LRC codes that generalizes the classical construction of Reed-Solomon codes was constructed in a recent paper by I. Tamo and…

Information Theory · Computer Science 2015-02-06 Itzhak Tamo , Alexander Barg , Sreechakra Goparaju , Robert Calderbank

We consider an ensemble of constant composition codes that are subsets of linear codes: while the encoder uses only the constant-composition subcode, the decoder operates as if the full linear code was used, with the motivation of…

Information Theory · Computer Science 2022-06-22 Neri Merhav , Georg Bocherer

In this paper, we construct the first families of asymmetric quantum convolutional codes (AQCC)'s. These new AQCC's are constructed by means of the CSS-type construction applied to suitable families of classical convolutional codes, which…

Quantum Physics · Physics 2016-10-05 Giuliano G. La Guardia

One of the most important and challenging problems in coding theory is to construct codes with best possible parameters and properties. The class of quasi-cyclic (QC) codes is known to be fertile to produce such codes. Focusing on QC codes…

Information Theory · Computer Science 2021-08-17 Dev Akre , Nuh Aydin , Matthew J. Harrington , Saurav R. Pandey

A method for construction of polar subcodes is presented, which aims on minimization of the number of low-weight codewords in the obtained codes, as well as on improved performance under list or sequential decoding. Simulation results are…

Information Theory · Computer Science 2017-05-04 Peter Trifonov , Grigorii Trofimiuk

We give an upper bound that relates the minimum weight of a nonzero componentwise product of codewords from some given number of linear codes, with the dimensions of these codes. Its shape is a direct generalization of the classical…

Information Theory · Computer Science 2016-11-18 Hugues Randriambololona

Linear codes are widely studied due to their applications in communication, cryptography, quantum codes, distributed storage and many other fields. In this paper, we use the trace and norm functions over finite fields to construct a family…

Information Theory · Computer Science 2024-04-30 Ziling Heng , Mengjie Yang , Yang Ming

Permutation codes are a class of structured vector quantizers with a computationally-simple encoding procedure based on sorting the scalar components. Using a codebook comprising several permutation codes as subcodes preserves the…

Information Theory · Computer Science 2015-03-13 Ha Q. Nguyen , Lav R. Varshney , Vivek K Goyal

Irreducible cyclic codes are one of the largest known classes of block codes which have been investigated for a long time. However, their weight distributions are known only for a few cases. In this paper, a class of irreducible cyclic…

Cryptography and Security · Computer Science 2013-09-06 Yun Song , Zhihui Li

Due to their fast decoding algorithms, quantum generalizations of low-density parity check, or LDPC, codes have been investigated as a solution to the problem of decoherence in fragile quantum states. However, the additional twisted inner…

Quantum Physics · Physics 2012-07-04 Jacob Farinholt

Recently, some infinite families of minimal and optimal binary linear codes were constructed from simplicial complexes by Hyun {\em et al.} We extend this construction method to arbitrary posets. Especially, anti-chains are corresponded to…

Information Theory · Computer Science 2020-08-18 Jong Yoon Hyun , Hyun Kwang Kim , Yansheng Wu , Qin Yue

This paper introduces a class of structured lowdensity parity-check (LDPC) codes whose parity check matrices are arrays of permutation matrices. The permutation matrices are obtained from Latin squares and form a finite field under some…

Information Theory · Computer Science 2010-04-09 Dung Viet Nguyen , Bane Vasic , Michael Marcellin , Shashi Kiran Chilappagari

Product codes are a class of quantum error correcting codes built from two or more constituent codes. They have recently gained prominence for a breakthrough yielding quantum low-density parity-check (qLDPC) codes with favorable scaling of…

Quantum Physics · Physics 2026-05-05 Shuyu Zhang , Tzu-Chieh Wei , Nathanan Tantivasadakarn

We define linear and semilinear isometry for general subspace codes, used for random network coding. Furthermore, some results on isometry classes and automorphism groups of known constant dimension code constructions are derived.

Information Theory · Computer Science 2014-06-20 Anna-Lena Trautmann

This paper aims to construct optimal quaternary additive codes with non-integer dimensions. Firstly, we propose combinatorial constructions of quaternary additive constant-weight codes, alongside additive generalized anticode construction.…

Information Theory · Computer Science 2024-11-12 Chaofeng Guan , Jingjie Lv , Gaojun Luo , Zhi Ma

The duals of cyclic codes with two zeros have been extensively studied, and their weight distributions have recently been evaluated in some cases. In this note, we determine the weight distribution of a certain new class of such codes by…

Combinatorics · Mathematics 2012-06-18 Tao Feng , Koji Momihara

Recently, the weight distributions of the duals of the cyclic codes with two zeros have been obtained for several cases. In this paper we solve one more special case. The problem of finding the weight distribution is transformed into a…

Number Theory · Mathematics 2012-10-17 Maosheng Xiong