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This paper gives upper bounds on the weight hierarchies of the latter class of codes. ... Linear codes may be classiÿed according to a set of chain and non-chain conditions, the extreme cases being codes satisfying the chain condition (due to Wei and Yang) and extremal, non-chain codes (due ... Acknowledgements The author wishes to thank prof. Torleiv KlHve for helpful comments and for suggesting the problem in the ÿrst place. ...doi:10.1016/s0012-365x(01)00131-5 fatcat:jksglclvczgkxheuou7wbm66nm
) Bounds on the weight hierarchies of extremal non-chain codes of dimension 4. ... Bounds on the weight hierarchies of such codes of dimension 4 are studied.” 98e:94028 94B05 Constantinescu, loana (D-MUTU; Munich); Heise, Werner (D-MUTU; Munich) On the concept of code-isomorphy. ...
Han (D-ESSN-EM; Essen) The determination of the chain good weight hierarchies with high dimension. (English summary) SIAM J. Discrete Math. 17 (2003), no. 2, 196-209 (electronic). ... known bounds on the minimum weight for linear codes over Fs; are constructed from conference matrices. ...
The X-codes are of minimum column distance 3, namely, they can correct either one column error or two column erasures. ... We present a new class of MDS array codes of size n 2 n (n a prime number) called X-code. ... In  we gave bounds on the weight hierarchies of extremal nonchain codes of dimension 4. ...doi:10.1109/18.746809 fatcat:35s4hw72lrhrljbjrtqa2nbqpy
Lecture Notes in Computer Science
In this paper we suggest one approach based on the weight hierarchy, and it allows us to conduct an extremely rapid computer search to prove that there are exactly two inequivalent [36, 8, 16] codes. ... The technique can also be used to gain new information about the weight hierarchy of the putative [72, 36, 16] code, but not yet enough to say if it exists or not. ... Every binary [36, 8, 16] code satisfies the chain condition. Proof. Consider a subcode D 4 30 of dimension 4 and weight 30. ...doi:10.1007/978-3-642-10868-6_4 fatcat:2eycysad4vfcfp74mfwfmouzpq
The codes of dimension 4 are collected in classes. The possible weight hierarchies in each class are given. For one class the details of the proofs are included. ... The weight hierarchy of a binary linear [n; k] code C is the sequence (d1; d2; : : : ; d k ) where dr is the smallest support of an r-dimensional subcode of C. ... The research was supported by The Norwegian Research Council and the National Science Foundation of China. ...doi:10.1016/s0012-365x(00)00411-8 fatcat:xirrhto2mzdkreh27dw3wr7qau
, Wende (PRC-ASBJ-SYC; Beijing) ; Kleve, Torleivy (N-BERG-I; Bergen) Weight hierarchies of extremal non-chain binary codes of dimension 4, (English summary) IEEE Trans. ... The possible weight hierarchies of such binary codes of dimension 4 are determined.” 99k:94046 94B05 Hamada, Noboru (J-OWU-AM; Osaka) On the nonexistence of some quaternary linear codes meeting the Griesmer ...
Recently, a class of fractal surface codes (FSCs), has been constructed on fractal lattices with Hausdorff dimension 2+ϵ, which admits a fault-tolerant non-Clifford CCZ gate. ... The latter can be mapped to the critical point of a zero-temperature confinement-Higgs transition on the fractal lattice, which is tunable via the Hausdorff dimension. ... The code used for the simulations and the data extracted are currently available upon request. Both will be made publicly available on GitHub shortly. ...arXiv:2201.03568v1 fatcat:edwdzgwwwzhptcevgh5k5qehcm
., Helge Tverberg A celebration of a life in mathematics (1}3) 1} 6 Schaathun , H.G., Upper bounds on weight hierarchies of extremal non-chain codes (1}3) 449}469 SchoK bel, A., see H. ... Kl+ve, On the second greedy weight for linear codes of dimension 3 (1}3) 171}187 Daneshgar, A., A.J.W. Hilton and P.D. ...doi:10.1016/s0012-365x(01)00341-7 fatcat:waxxkib62rgktblf37dt666hiq
We introduce quantum pin codes: a class of quantum CSS codes. Quantum pin codes are a generalization of quantum color codes and Reed-Muller codes and share a lot of their structure and properties. ... We study examples of these codes and their properties. ... One can also prove the following general lower bound on the distance of pin codes. Proposition 7 (Distance at least 4). ...arXiv:1906.11394v3 fatcat:bk3djrn5g5ayrjaojgoixeo72y
The proposed lower bound estimate is used to construct several heuristic algorithms and to evaluate their quality on a variety of generated and real-life data sets. ... For the case of connecting trees with the given sequence of vertex degrees, the cost of the optimal tree is shown to be bounded from below by the solution of a semidefinite optimization program with bilinear ... The quality of the lower bound is evaluated on a number of generated flow matrices with dimension from 10 to 1000 and on the selected real-life origindestination matrices with dimension varying from 12 ...arXiv:1808.06199v2 fatcat:v5l2zfmgrfa3th7vlwzbgthguu
to achieve this state depend on the project's scale. ... In particular, we found that: (a) developers form scale-free networks, in which the majority of coordination requirements arise among an extremely small number of developers, (b) developers tend to accumulate ... Acknowledgements This work has been supported by the German Research Foundation (AP 206/4, AP 206/5, AP 206/6). ...arXiv:1510.06988v2 fatcat:uizeghe33jevtehg4ebmrgkhgq
code. ... Unfortunately, optimization usually comes at the cost of programmer pain and code complexity, as computation must be reorganized to achieve memory efficiency and parallelism. ... Acknowledgments This work was partially funded by the Quanta T-Party, NSF grants 0964004, 0964218, and 0832997, DOE award DE-SC0005288, and gifts from Cognex and Adobe. ...doi:10.1145/2185520.2185528 fatcat:mdfbhjwc5zatfoq4mt6p3j7m7a
code. ... Unfortunately, optimization usually comes at the cost of programmer pain and code complexity, as computation must be reorganized to achieve memory efficiency and parallelism. ... Acknowledgments This work was partially funded by the Quanta T-Party, NSF grants 0964004, 0964218, and 0832997, DOE award DE-SC0005288, and gifts from Cognex and Adobe. ...doi:10.1145/2185520.2335383 fatcat:smf4xdhjpzhn3ggl2qyilol22y
Minimal trellises for linear codes are obtained by forming the product of elementary trellises corresponding to the one-dimensional subcodes generated by atomic codewords. ... A correspondence between minimal linear block code trellises and con gurations of non-attacking rooks on a triangular chess board is established and used to show that the number of distinct minimal linear ... Trott for prompting us to discover the example described in the Appendix. ...doi:10.1109/18.476317 fatcat:qmjwknh4rzfgvjedigcwo2jowu
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