New optimal asymmetric quantum codes and quantum convolutional codes derived from constacyclic codes
Sign Up to like & getrecommendations! Published in 2019 at "Quantum Information Processing"
DOI: 10.1007/s11128-018-2156-7
Abstract: In this paper, some families of asymmetric quantum codes and quantum convolutional codes that satisfy the quantum Singleton bound are constructed by utilizing constacyclic codes with length $$n=\frac{q^2+1}{10h}$$n=q2+110h, where q is an odd prime power… read more here.
Keywords: quantum convolutional; convolutional codes; codes quantum; asymmetric quantum ... See more keywords
Concatenated linear systems over rings and their application to construction of concatenated families of convolutional codes
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DOI: 10.1016/j.laa.2017.12.009
Abstract: Abstract We present a generalization of the theory of concatenated linear systems to commutative rings with identity. Moreover, we highlight sufficient conditions to obtain reachable and observable concatenated linear systems. This approach provides us with… read more here.
Keywords: convolutional codes; concatenated families; concatenated linear; systems rings ... See more keywords
Series concatenation of 2D convolutional codes by means of input-state-output representations
Sign Up to like & getrecommendations! Published in 2018 at "International Journal of Control"
DOI: 10.1080/00207179.2017.1410573
Abstract: ABSTRACT In this paper, we investigate the properties of two-dimensional (2D) convolutional codes which are obtained from series concatenation of two 2D convolutional codes. For this purpose, we confine ourselves to dealing with finite-support 2D… read more here.
Keywords: series concatenation; convolutional codes; state output; input state ... See more keywords
Edge-Coloring Technique to Analyze Elementary Trapping Sets of Spatially-Coupled LDPC Convolutional Codes
Sign Up to like & getrecommendations! Published in 2020 at "IEEE Communications Letters"
DOI: 10.1109/lcomm.2019.2962671
Abstract: In this letter, for the first time, an edge-coloring technique is proposed to characterize a certain elementary trapping set (ETS) and to obtain sufficient conditions to avoid small ETSs from occurrence in the Tanner graph… read more here.
Keywords: coloring technique; convolutional codes; ldpc convolutional; elementary trapping ... See more keywords
Rosenthal’s Decoding Algorithm for Certain 1-Dimensional Convolutional Codes
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DOI: 10.1109/tit.2019.2921370
Abstract: The performance of Rosenthal’s decoding algorithm is measured when it is applied to certain family of 1-dimensional MDS convolutional codes. It is shown that the performance of this algorithm depends on the algebraic structure of… read more here.
Keywords: algorithm certain; rosenthal decoding; decoding algorithm; certain dimensional ... See more keywords
A Construction of Maximum Distance Profile Convolutional Codes With Small Alphabet Sizes
Sign Up to like & getrecommendations! Published in 2023 at "IEEE Transactions on Information Theory"
DOI: 10.1109/tit.2023.3236425
Abstract: Convolutional codes are essential in a wide range of practical applications due to their efficient non-algebraic decoding algorithms. In this paper, we first propose a new family of matrices over finite fields by combining Vandermonde… read more here.
Keywords: distance profile; maximum distance; alphabet; convolutional codes ... See more keywords
On the left primeness of some polynomial matrices with applications to convolutional codes
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Algebra and Its Applications"
DOI: 10.1142/s0219498821502078
Abstract: Maximum distance profile (MDP) convolutional codes have the property that their column distances are as large as possible for given rate and degree. There exists a well-known criterion to check whether a code is MDP… read more here.
Keywords: left primeness; primeness polynomial; divides delta; polynomial matrices ... See more keywords