Abstract
The study of codes for the Niederreiter-Rosenbloom-Tsfasman metric has a long history of parallel developments.
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References
M.M.S. Alves, A standard form for generator matrices with respect to the Niederreiter-Rosenbloom-Tsfasman metric, in 2011 IEEE Information Theory Workshop, ITW 2011 (2011), pp. 486–489
A. Barg, W. Park, On linear ordered codes. Moscow Math. J. 15, 679–702 (2015)
A. Barg, P. Purkayastha, Bounds on ordered codes and orthogonal arrays, in IEEE International Symposium on Information Theory Proceedings (2007), pp. 331–335
A. Barg, P. Purkayastha, Bounds on ordered codes and orthogonal arrays. Moscow Math. J. 9(2), 211–243 (2009)
A. Barg, L.V. Felix, M. Firer, M.V.P. Spreafico, Linear codes on posets with extension property. Discrete Math. 317, 1–13 (2014)
R.A. Brualdi, J.S. Graves, K.M. Lawrence, Codes with a poset metric. Discrete Math. 147(1–3), 57–72 (1995)
A.G. Castoldi, E.L.M. Carmelo, The covering problem in Rosenbloom-Tsfasman spaces. Electron. J. Comb. 22(3), 1–18 (2015)
S. Dougherty, K. Shiromoto, Maximum distance codes in Mat n,s(Z k) with a non-Hamming metric and uniform distributions. Des. Codes Crypt. 33(1), 45–61 (2004)
S.T. Dougherty, M.M. Skriganov, MacWilliams duality and the Rosenbloom-Tsfasman metric. Moscow Math. J. 2(1), 81–97 (2002)
S.T. Dougherty, M.M. Skriganov, Maximum distance separable codes in the ρ metric over arbitrary alphabets. J. Algebraic Comb. 16, 71–81 (2002)
C. Feyling, Punctured maximum distance separable codes. Electron. Lett. 29(5), 470–471 (1993)
H. Hasse, Theorie der höheren differentiale in einem algebraischen funktionenkörper mit vollkommenem konstantenkörper bei beliebiger charakteristik. J. Reine Angew. Math. 175, 50–54 (1936)
W.C. Huffman, V. Pless, Fundamentals of Error-Correcting Codes (Cambridge University Press, Cambridge, 2003)
J.Y. Hyun, H.K. Kim, Maximum distance separable poset codes. Des. Codes Crypt. 48(3), 247–261 (2008)
J.Y. Hyun, Y. Lee, MDS poset-codes satisfying the asymptotic Gilbert-Varshamov bound in Hamming weights. IEEE Trans. Inf. Theory 57(12), 8021–8026 (2011)
W.C. Lidl, H. Niederreiter, Finite Fields, 2nd edn. (Cambridge University Press, Cambridge, 1996)
H. Niederreiter, Point sets and sequences with small discrepancy. Monatshefte für Mathematik 104(4), 273–337 (1987)
H. Niederreiter, Orthogonal arrays and other combinatorial aspects in the theory of uniform point distributions in unit cubes. Discrete Math. 106–107, 361–367 (1992)
M. Ozen, I. Siap, Linear codes over \(\mathbb {F}_q[u]/(u^s)\) with respect to the Rosenbloom-Tsfasman metric. Des. Codes Crypt. 38(1), 17–29 (2006)
L. Panek, M. Firer, M.M.S. Alves, Classification of Niederreiter-Rosenbloom-Tsfasman block codes. IEEE Trans. Inf. Theory 56(10), 5207–5216 (2010)
M.Y. Rosenbloom, M.A. Tsfasman, Codes for the m-metric. Problems Inf. Transm. 33, 45–52 (1997)
M.M. Skriganov, Coding theory and uniform distributions. St. Petersburg Math. J. 13, 301–337 (2002)
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Firer, M., S. Alves, M.M., Pinheiro, J.A., Panek, L. (2018). Disjoint Chains with Equal Length: The Niederreiter-Rosenbloom-Tsfasman Metric. In: Poset Codes: Partial Orders, Metrics and Coding Theory. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-93821-9_4
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