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A conjugate code pair is defined as a pair of linear codes either of which contains the dual of the other. A conjugate code pair represents the essential structure of the corresponding Calderbank-Shor-Steane (CSS) quantum code. It is known…

Quantum Physics · Physics 2007-05-23 Mitsuru Hamada

In this paper, we propose new coupled codes constructed by overlapping circular spatially-coupled low-density parity-check (SC-LDPC) codes, which show better asymptotic and finite-length decoding performance compared to the conventional…

Information Theory · Computer Science 2018-03-28 Heeyoul Kwak , Bohwan Jun , Pilwoong Yang , Jong-Seon No , Dong-Joon Shin

Linear codes with complementary-duals (LCD) are linear codes that intersect with their dual trivially. Multinegacirculant codes of index $2$ that are LCD are characterized algebraically and some good codes are found in this family. Exact…

Information Theory · Computer Science 2017-03-10 Adel Alahmadi , Cem Güneri , Buket Özkaya , Hatoon Shoaib , Patrick Solé

Linear codes with complementary duals (abbreviated LCD) are linear codes whose intersection with their dual are trivial. When they are binary, they play an important role in armoring implementations against side-channel attacks and fault…

Information Theory · Computer Science 2017-03-17 Claude Carlet , Sihem Mesnager , Chunming Tang , Yanfeng Qi

A conjugate code pair is defined as a pair of linear codes either of which contains the dual of the other. A conjugate code pair represents the essential structure of the corresponding Calderbank-Shor-Steane (CSS) quantum error-correcting…

Information Theory · Computer Science 2007-07-13 Mitsuru Hamada

Subspace codes were introduced in order to correct errors and erasures for randomized network coding, in the case where network topology is unknown (the noncoherent case). Subspace codes are indeed collections of subspaces of a certain…

Information Theory · Computer Science 2012-02-03 Hessam Mahdavifar , Alexander Vardy

Linear complementary-dual (LCD for short) codes are linear codes that intersect with their duals trivially. LCD codes have been used in certain communication systems. It is recently found that LCD codes can be applied in cryptography. This…

Information Theory · Computer Science 2017-02-28 Bocong Chen , Hongwei Liu

Two families of complementary codes over finite fields $\mathbb{F}_q$ are studied, where $q=r^2$ is square: i) Hermitian complementary dual linear codes, and ii) trace Hermitian complementary dual subfield linear codes. Necessary and…

Information Theory · Computer Science 2017-10-13 Kriangkrai Boonniyom , Somphong Jitman

For a regular coupled cell network, synchrony subspaces are the polydiagonal subspaces that are invariant under the network adjacency matrix. The complete lattice of synchrony subspaces of an $n$-cell regular network can be seen as an…

Dynamical Systems · Mathematics 2020-07-16 Hiroko Kamei , Haibo Ruan

In this paper, we study linear complementary pairs (LCP) of codes over finite non-commutative local rings. We further provide a necessary and sufficient condition for a pair of codes $(C,D)$ to be LCP of codes over finite non-commutative…

Information Theory · Computer Science 2024-06-25 Sanjit Bhowmick , Xiusheng Liu

Non-overlapping codes are block codes that have arisen in diverse contexts of computer science and biology. Applications typically require finding non-overlapping codes with large cardinalities, but the maximum size of non-overlapping codes…

Information Theory · Computer Science 2024-01-11 Lidija Stanovnik , Miha Moškon , Miha Mraz

An $(r,M,2\delta;k)_q$ constant--dimension subspace code, $\delta >1$, is a collection $\cal C$ of $(k-1)$--dimensional projective subspaces of ${\rm PG(r-1,q)}$ such that every $(k-\delta)$--dimensional projective subspace of ${\rm…

Combinatorics · Mathematics 2014-11-14 Antonio Cossidente , Francesco Pavese

A linear code with a complementary dual (or LCD code) is defined to be a linear code $C$ whose dual code $C^{\perp}$ satisfies $C \cap C^{\perp}$= $\left\{ \mathbf{0}\right\} $. Let $LCD{[}n,k{]}$ denote the maximum of possible values of…

Information Theory · Computer Science 2017-01-17 Lucky Galvez , Jon-Lark Kim , Nari Lee , Young Gun Roe , Byung-Sun Won

A covering code is a set of codewords with the property that the union of balls, suitably defined, around these codewords covers an entire space. Generally, the goal is to find the covering code with the minimum size codebook. While most…

Information Theory · Computer Science 2020-05-26 Andreas Lenz , Cyrus Rashtchian , Paul H. Siegel , Eitan Yaakobi

In this paper, we propose a class of linear codes and obtain their weight distribution. Some of these codes are almost optimal. Moreover, several classes of constant composition codes(CCCs) are constructed as subcodes of linear codes.

Information Theory · Computer Science 2017-06-28 Long Yu , Xiusheng Liu

In network coding, a flag code is a collection of flags, that is, sequences of nested subspaces of a vector space over a finite field. Due to its definition as the sum of the corresponding subspace distances, the flag distance parameter…

Information Theory · Computer Science 2021-12-01 Clementa Alonso-González , Miguel Ángel Navarro-Pérez

A linear code is linear complementary dual (LCD) if it meets its dual trivially. LCD codes have been a hot topic recently due to Boolean masking application in the security of embarked electronics (Carlet and Guilley, 2014). Additive codes…

Information Theory · Computer Science 2022-07-06 Minjia Shi , Na Liu , Jon-Lark Kim , Patrick Solé

This paper provides new constructions and lower bounds for subspace codes, using Ferrers diagram rank-metric codes from matchings of the complete graph and pending blocks. We present different constructions for constant dimension codes with…

Information Theory · Computer Science 2015-05-08 Natalia Silberstein , Anna-Lena Trautmann

A subspace arrangement in a vector space is a finite collection of vector subspaces. Similarly, a configuration of linear spaces in a projective space is a finite collection of linear subspaces. In this paper we study the degree 2 part of…

Algebraic Geometry · Mathematics 2009-10-07 E. Carlini , M. V. Catalisano , A. V. Geramita

A conjugate code pair is defined as a pair of linear codes such that one contains the dual of the other. The conjugate code pair represents the essential structure of the corresponding Calderbank-Shor-Steane (CSS) quantum code. It is argued…

Quantum Physics · Physics 2009-01-21 Mitsuru Hamada