Kirkman systems and their application in perpendicular magnetic recording

Vasić, Bane; Kurtas, E.; Kuznetsov, Alexander V.

doi:10.1109/tmag.2002.1017760

Cited by 27 publications

(22 citation statements)

References 22 publications

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“…An STS is r-sparse if and only if it contains no (k + 2, k)-configuration for every 1 < k ≤ r. As well as in combinatorial design theory, 4-and 5-sparse STSs are also important in some applications to information theory (see, for example, Chee, Colbourn and Ling [6]; Johnson and Weller [22]; Vasic, Kurtas and Kuznetsov [34]; and Vasic and Milenkovic [33]), and hence constructions of an r-sparse STS are studied extensively from both sides.…”

Section: ) Let L(k L) Be the Family Of All Nonisomorphic 3-uniform Hmentioning

confidence: 99%

Nonexistence of sparse triple systems over abelian groups and involutions

Fujiwara

2007

J Algebr Comb

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In 1973 Paul Erdős conjectured that there is an integer v 0 (r) such that, for every v > v 0 (r) and v ≡ 1, 3 (mod 6), there exists a Steiner triple system of order v, containing no i blocks on i + 2 points for every 1 < i ≤ r. Such an STS is said to be r-sparse. In this paper we consider relations of automorphisms of an STS to its sparseness. We show that for every r ≥ 13 there exists no point-transitive r-sparse STS over an abelian group. This bound and the classification of transitive groups give further nonexistence results on block-transitive, flag-transitive, 2-transitive, and 2-homogeneous STSs with high sparseness. We also give stronger bounds on the sparseness of STSs having some particular automorphisms with small groups. As a corollary of these results, it is shown that various well-known automorphisms, such as cyclic, 1-rotational over arbitrary groups, and involutions, prevent an STS from being high-sparse.

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Section: ) Let L(k L) Be the Family Of All Nonisomorphic 3-uniform Hmentioning

confidence: 99%

Nonexistence of sparse triple systems over abelian groups and involutions

Fujiwara

2007

J Algebr Comb

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“…Recently, Johnson and Weller [16], as well as Vasic [32], presented almost identical approaches to the design of LDPC codes using combinatorial designs. The ideas in [32] and [33] were further developed in the series of papers [34]- [37]. MacKay and Davey [38] also used Steiner systems (a subclass of BIBDs) to construct Gallager codes.…”

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confidence: 99%

Combinatorial Constructions of Low-Density Parity-Check Codes for Iterative Decoding

Vasić

Milenković

2004

IEEE Trans. Inform. Theory

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Abstract-This paper introduces several new combinatorial constructions of low-density parity-check (LDPC) codes, in contrast to the prevalent practice of using long, random-like codes. The proposed codes are well structured, and unlike random codes can lend themselves to a very low-complexity implementation. Constructions of regular Gallager codes based on cyclic difference families, cycle-invariant difference sets, and affine 1-configurations are introduced. Several constructions of difference families used for code design are presented, as well as bounds on the minimal distance of the codes based on the concept of a generalized Pasch configuration.

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“…LDPC kod dužine N = 4732, sa M = 169 bita za proveru parnosti i težinom kolona 3, baziran je na Kirkmanovim sistemima [132].…”

Section: Ldpc -Mtr Kod Na E 2 Pr4 Otoh Kanaluunclassified

“…LDPC -MTR veza je razmatrana na E 2 PR4 OTOH i TTTH modelu kanala koristeći LDPC kodne brzine R = 0,96 [132] i dobro poznati 4/5 MTR (2, k = 8) kod [1].…”

Kirkman systems and their application in perpendicular magnetic recording

Cited by 27 publications

References 22 publications

Nonexistence of sparse triple systems over abelian groups and involutions

Nonexistence of sparse triple systems over abelian groups and involutions

Combinatorial Constructions of Low-Density Parity-Check Codes for Iterative Decoding

Soft-decision decoding of MTR codes over magnetic recording channels

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