On Rosenbloom and Tsfasman's generalization of the Hamming space

Quistorff, Jörn

doi:10.1016/j.disc.2007.01.005

Cited by 16 publications

(9 citation statements)

References 10 publications

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“…We now review the RT metric according to the approach in Brualdi et al (1995), which differs from that in Quistorff (2007) , Rosenbloom and Tsfasman (1997), Yildiz et al (2010). Let P be a finite partial ordered set (poset) and denote its partial order relation by .…”

Section: Preliminaries: Rt Metric and Spheresmentioning

confidence: 99%

Partial sums of binomials, intersecting numbers, and the excess bound in Rosenbloom–Tsfasman space

2019

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In this work, the sphere-covering bound on covering codes in Rosenbloom-Tsfasman spaces (RT spaces) is improved by generalizing the excess counting method. The approach focuses on studying the parity of a Rosenbloom-Tsfasman sphere (RT sphere) and the parity of the intersection of two RT spheres. We connect the parity of an RT sphere with partial sums of binomial coefficients and p-adic valuation of binomial coefficients. The intersection number of RT spaces is introduced and we determinate its parity under some conditions. Numerical applications of the method are discussed. Keywords Rosenbloom-Tsfasman metric • Covering code • Bounds on code • Sum of binomials • Congruence Mathematics Subject Classification 94B25 • 05A10 • 05A19 • 06A06 Communicated by Masaaki Harada.

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Section: Preliminaries: Rt Metric and Spheresmentioning

confidence: 99%

Partial sums of binomials, intersecting numbers, and the excess bound in Rosenbloom–Tsfasman space

2019

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“…The fact that there are relatively many codes with such properties is what first attracted the attention to poset metrics. For perfect or MDS codes with poset metrics see [9,47,53,49,24,72] and [48], among others.…”

Section: )mentioning

confidence: 99%

Alternative Metrics

Firer

2019

Preprint

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“…The NRT metric is more appropriate for the correction of random errors that occur with high probability in the first coordinates. Since its definition several coding-theoretic questions with respect to the Niederreiter Rosenbloom-Tsfasman metric have been investigated, such as bounds [1,11], weight distribution and MacWilliams Identities [2,9,22], self-dual codes [25,26], MDS codes [16,23,24], burst error enumeration [8,21], BCH codes [28], and decoding [18,20,27].…”

Section: Introductionmentioning

confidence: 99%

Bounds on Binary Niederreiter-Rosenbloom-Tsfasman LCD codes

Santos¹

2023

Preprint

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Linear complementary dual codes (LCD codes) are codes whose intersections with their dual codes are trivial. These codes were introduced by Massey in 1992. LCD codes have wide applications in data storage, communication systems and cryptography. Niederreiter-Rosenbloom-Tsfasman LCD codes (NRT-LCD codes) were introduced by Heqian, Guangku and Wei as a generalization of LCD codes for the NRT metric space Mn,s(Fq). In this paper, we study LCD[n × s, k], the maximum minimum NRT distance among all binary [n × s, k] NRT-LCD codes. We prove the existence (non-existence) of binary maximum distance separable NRT-LCD codes in M1,s(F2). We present a linear programming bound for binary NRT-LCD codes in Mn,2(F2). We also give two methods to construct binary NRT-LCD codes.

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On Rosenbloom and Tsfasman's generalization of the Hamming space

Cited by 16 publications

References 10 publications

Partial sums of binomials, intersecting numbers, and the excess bound in Rosenbloom–Tsfasman space

Partial sums of binomials, intersecting numbers, and the excess bound in Rosenbloom–Tsfasman space

Alternative Metrics

Bounds on Binary Niederreiter-Rosenbloom-Tsfasman LCD codes

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