(v, k, λ) Configurations and self-dual codes

Bhargava, V.K.; Stein, J.

doi:10.1016/s0019-9958(75)90350-2

Cited by 18 publications

(3 citation statements)

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“…Designs and codes are very closely connected combinatorial entities, since one can be used to construct the other. For example, codewords of fixed weight in many codes, including the Golay code and the class of quadratic residue codes, support designs (see, for example, [29] and [30]). On the other hand, the incidence matrix of a design defines a nonlinear code if the rows of the matrix are viewed as codewords [31].…”

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confidence: 99%

Combinatorial constructions of low-density parity check codes for iterative decoding

Vasić¹

Proceedings IEEE International Symposium on Information 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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confidence: 99%

Combinatorial constructions of low-density parity check codes for iterative decoding

Vasić¹

Proceedings IEEE International Symposium on Information Theory,

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“…If each t-element subset is contained in exactly λ blocks, the underlying design is known as t-design. An example of a 5-design is the extended ternary Golay code (see [3]). However, the codes based on t-designs (t>2) have short cycles, and therefore we will restrict ourselves to the 2-designs, i.e.…”

Section: Steiner Systems and Their Equivalence With Bipartite Graphsmentioning

confidence: 99%

“…The concept of combinatorial designs is well known, and their relation to coding theory is profound. Many classes of codes including extended Golay codes and quadratic residue QR codes can be interpreted as designs (see [3]). Using combinatorial designs for establishing bounds on minimum distance of LDPC codes has been recently proposed by MacKay and Davey [37].…”

Section: Introductionmentioning

confidence: 99%

Structured iteratively decodable codes based on Steiner systems and their application in magnetic recording

Vasić

GLOBECOM'01. IEEE Global Telecommunications Conference (Cat. No.01CH37270)

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This paper introduces a combinatorial construction of a class of iteratively decodable codes, an approach diametrically opposed to the prevalent practice of using large, random-like codes. Our codes are wellstructured and, unlike random codes, can lend themselves to a very low complexity implementation. A systematic way of constructing codes based on Steiner systems and the Z Z v , group is presented, and a hardware efficient encoding algorithm is proposed. A substantial performance improvement of high-rate Steiner codes over the existing schemes used in magnetic recording systems is demonstrated. .

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Design and Analysis of Low‐Density Parity‐Check Codes for Applications to Perpendicular Recording Channels

Kurtas

Kuznetsov

Vasić

2003

Wiley Encyclopedia of Telecommunications

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(v, k, λ) Configurations and self-dual codes

Cited by 18 publications

References 3 publications

Combinatorial constructions of low-density parity check codes for iterative decoding

Combinatorial constructions of low-density parity check codes for iterative decoding

Structured iteratively decodable codes based on Steiner systems and their application in magnetic recording

Design and Analysis of Low‐Density Parity‐Check Codes for Applications to Perpendicular Recording Channels

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