Results 1 to 10 of about 1,066,179 (25)
IEEE Transactions on Information Theory, volume 59, number 11,
pages 7386-7404, 2013, 2011 In network coding a constant dimension code consists of a set of k-dimensional subspaces of F_q^n. Orbit codes are constant dimension codes which are defined as orbits of a subgroup of the general linear group, acting on the set of all subspaces of F_q^n. If the acting group is cyclic, the corresponding orbit codes are called cyclic orbit codes.
arxiv +1 more source
Universal codes of the natural numbers [PDF]
Logical Methods in Computer Science, Volume 9, Issue 3 (August 29,
2013) lmcs:975, 2013 A code of the natural numbers is a uniquely-decodable binary code of the natural numbers with non-decreasing codeword lengths, which satisfies Kraft's inequality tightly. We define a natural partial order on the set of codes, and show how to construct effectively a code better than a given sequence of codes, in a certain precise sense.
arxiv +1 more source
On generalized quasi-cyclic codes over $\mathbb{Z}_4$ [PDF]
arXiv, 2022 Based on good algebraic structures and practicabilities, generalized quasi-cyclic (GQC) codes play important role in coding theory. In this paper, we study some results on GQC codes over $\mathbb{Z}_4$ including the normalized generating set, the minimum generating set and the normalized generating set of their dual codes.
arxiv
Information sets from defining sets for Reed-Muller codes of first and second order [PDF]
IEEE Trans. Inform. Theory, 64 (10) (2018) 6484-6497Reed-Muller codes belong to the family of affine-invariant codes. As such codes they have a defining set that determines them uniquely, and they are extensions of cyclic group codes. In this paper we identify those cyclic codes with multidimensional abelian codes and we use the techniques introduced in \cite{BS} to construct information sets for them ...
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A Construction of Quantum Stabilizer Codes Based on Syndrome Assignment by Classical Parity-Check Matrices [PDF]
IEEE Transactions on Information Theory, 57(10), 7163 - 7179,
(2011),, 2007 In quantum coding theory, stabilizer codes are probably the most important class of quantum codes. They are regarded as the quantum analogue of the classical linear codes and the properties of stabilizer codes have been carefully studied in the literature.
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Online Versus Offline Rate in Streaming Codes for Variable-Size Messages [PDF]
, 2020 One pervasive challenge in providing a high quality-of-service for live communication is to recover lost packets in real-time. Streaming codes are a class of erasure codes that are designed for such strict, low-latency streaming communication settings.
arxiv +1 more source
New entanglement-assisted MDS quantum codes from constacyclic codes [PDF]
Quantum Inf. Process. (2019), 2018 Construction of good quantum codes via classical codes is an important task for quantum information and quantum computing. In this work, by virtue of a decomposition of the defining set of constacyclic codes we have constructed eight new classes of entanglement-assisted quantum maximum distance separable codes.
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A Practical Approach to Polar Codes [PDF]
arXiv, 2011 In this paper, we study polar codes from a practical point of view. In particular, we study concatenated polar codes and rate-compatible polar codes. First, we propose a concatenation scheme including polar codes and Low-Density Parity-Check (LDPC) codes.
arxiv
A new class of codes for Boolean masking of cryptographic computations [PDF]
, 2011 We introduce a new class of rate one-half binary codes: {\bf complementary information set codes.} A binary linear code of length $2n$ and dimension $n$ is called a complementary information set code (CIS code for short) if it has two disjoint information sets. This class of codes contains self-dual codes as a subclass.
arxiv +1 more source
Galois LCD Codes over Finite Fields [PDF]
arXiv, 2017 In this paper, we study the complementary dual codes in more general setting (which are called Galois LCD codes) by a uniform method. A necessary and sufficient condition for linear codes to be Galois LCD codes is determined, and constacyclic codes to be Galois LCD codes are characterized.
arxiv