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Related papers: New Constant-Weight Codes from Propagation Rules

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For the past decades, linear codes with few weights have been widely studied, since they have applications in space communications, data storage and cryptography. In this paper, a class of binary linear codes is constructed and their weight…

Information Theory · Computer Science 2016-02-03 Fei Li , Yang Yan , Qiuyan Wang , Tongjiang Yan

Some new Gold type codes of higher relative dimension are introduced. Their weight distribution is determined.

Information Theory · Computer Science 2015-06-11 Chunlei Liu

In this paper, we investigate the symbol-pair weight distributions of MDS codes and simplex codes over finite fields. Furthermore, the result shows that all the nonzero codewords of simplex codes have the same symbol $b$-weight and…

Information Theory · Computer Science 2019-11-07 Junru Ma , Jinquan Luo

Some new Kasami type codes of higher relative dimension is introduced. Their weight distribution is determined.

Information Theory · Computer Science 2015-06-11 Chunlei Liu

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…

Information Theory · Computer Science 2007-10-15 Russell Bent , Michael Schear , Lane A. Hemaspaandra , Gabriel Istrate

From cosets of binary Hamming codes we construct diameter perfect constant-weight ternary codes with weight $n-1$ (where $n$ is the code length) and distances 3 and 5. The class of distance 5 codes has parameters unknown before. Keywords:…

Combinatorics · Mathematics 2009-08-03 Denis Krotov

We demonstrate propagation rules of subsystem code constructions by extending, shortening and combining given subsystem codes. Given an $[[n,k,r,d]]_q$ subsystem code, we drive new subsystem codes with parameters $[[n+1,k,r,\geq d]]_q$,…

Quantum Physics · Physics 2008-11-11 Salah A. Aly

We present a new propagation rule for CSS codes. Starting with a CSS code $[\![n,k,d]\!]_q$, we construct a CSS code with parameters $[\![n-2,k,d-1]\!]_q$. In general, one would only obtain a code with parameters $[\![n-2,k,d-2]\!]_q$. The…

Quantum Physics · Physics 2023-10-06 Markus Grassl

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

Information Theory · Computer Science 2016-02-05 Chunming Tang , Can Xiang , Keqin Feng

We introduce the class of multiply constant-weight codes to improve the reliability of certain physically unclonable function (PUF) response. We extend classical coding methods to construct multiply constant-weight codes from known $q$-ary…

Information Theory · Computer Science 2014-01-17 Yeow Meng Chee , Zouha Cherif , Jean-Luc Danger , Sylvain Guilley , Han Mao Kiah , Jon-Lark Kim , Patrick Solé , Xiande Zhang

We present a novel technique for encoding and decoding constant weight binary codes that uses a geometric interpretation of the codebook. Our technique is based on embedding the codebook in a Euclidean space of dimension equal to the weight…

Combinatorics · Mathematics 2014-09-17 Chao Tian , Vinay A. Vaishampayan , N. J. A. Sloane

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…

Information Theory · Computer Science 2021-06-08 Fei Li , Xiumei Li

Inspired by the Z2Z4-additive codes, linear codes over Z2^r x(Z2+uZ2)^s have been introduced by Aydogdu et al. more recently. Although these family of codes are similar to each other, linear codes over Z2^r x(Z2+uZ2)^s have some advantages…

Information Theory · Computer Science 2017-04-25 Ismail Aydogdu

Recently, linear codes constructed by defining sets have attracted a lot of study, and many optimal linear codes with a few weights have been produced. The objective of this paper is to present a class of binary linear codes with three…

Information Theory · Computer Science 2016-08-22 Yang Yan , Fei Li , Qiuyan Wang

Motivated by applications in polymer-based data storage we introduced the new problem of characterizing the code rate and designing constant-weight binary $B_2$-sequences. Binary $B_2$-sequences are collections of binary strings of length…

Information Theory · Computer Science 2023-03-24 Jin Sima , Yun-Han Li , Ilan Shomorony , Olgica Milenkovic

Linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, several classes of $p$-ary linear codes with two or three weights are constructed…

Information Theory · Computer Science 2015-10-20 Zhengchun Zhou , Nian Li , Cuiling Fan , Tor Helleseth

In this expository paper we show how one can, in a uniform way, calculate the weight distributions of some well-known binary cyclic codes. The codes are related to certain families of curves, and the weight distributions are related to the…

Number Theory · Mathematics 2016-09-06 René Schoof

We present an encoding and decoding scheme for constant weight sequences, that is, given an information sequence, the construction results in a sequence of specific weight within a certain range. The scheme uses a prefix design that is…

Information Theory · Computer Science 2017-06-06 Elie Ngomseu Mambou , Theo G. Swart

Multiply constant-weight codes (MCWCs) have been recently studied to improve the reliability of certain physically unclonable function response. In this paper, we give combinatorial constructions for MCWCs which yield several new infinite…

Information Theory · Computer Science 2014-11-11 Yeow Meng Chee , Han Mao Kiah , Hui Zhang , Xiande Zhang

This paper provides new and improved Singleton-like bounds for Lee metric codes over integer residue rings. We derive the bounds using various novel definitions of generalized Lee weights based on different notions of a support of a linear…

Information Theory · Computer Science 2023-07-13 Jessica Bariffi , Violetta Weger