Generalized Reed - Solomon codes from algebraic geometry

Lint, JH van; Springer, T. A.

doi:10.1109/tit.1987.1057320

Cited by 58 publications

(18 citation statements)

References 7 publications

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“…However, if one wishes to construct a single "basic" ramp scheme from an AG code, it of course suffices to determine minimum distance and dual distance of the obtained codes. This is what we do here, basing our presentation on the simple treatment of AG codes given by van Lint [17]. The resulting ramp scheme has the same thresholds as the schemes in [5].…”

Section: Codes and Ramp Schemesmentioning

confidence: 65%

A simple combinatorial treatment of constructions and threshold gaps of ramp schemes

Paterson

Stinson

2013

Cryptogr. Commun.

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We give easy proofs of some recent results concerning threshold gaps in ramp schemes. We then generalise a construction method for ramp schemes employing error-correcting codes so that it can be applied using nonlinear (as well as linear) codes. Finally, as an immediate consequence of these results, we provide a new explicit bound on the the minimum length of a code having a specified distance and dual distance.

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Section: Codes and Ramp Schemesmentioning

confidence: 65%

A simple combinatorial treatment of constructions and threshold gaps of ramp schemes

Paterson

Stinson

2013

Cryptogr. Commun.

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“…Substituting the explicit form of the points we get These equations can further be developed to give specific forms as shown in (1) and (2). From the structure of (2), it comes naturally to define a matrix as in (3) to convert the expression into a matrix multiplication. Similarly we define a matrix A as…”

Section: Hermitian Codes and Syndrome Computationmentioning

confidence: 99%

“…In recent years, an important class of one-point AG codes, called Hermitian codes, has been frequently discussed [3]- [6].…”

Section: Introductionmentioning

confidence: 99%

A Low Complexity Algorithm and Architecture for Systematic Encoding of Hermitian Codes

Agarwal

Koetter²,

Popovici

2007

2007 IEEE International Symposium on Information Theory

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Abstract-We present an algorithm for systematic encoding of Hermitian codes. For a Hermitian code defined over GF (q 2 ), the proposed algorithm achieves a run time complexity of O(q 2 ) and is suitable for VLSI implementation. The encoder architecture uses as main blocks q varying-rate Reed-Solomon encoders and achieves a space complexity of O(q 2 ) in terms of finite field multipliers and memory elements.

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“…The interest in this topic is demonstrated by the number of survey articles [1,6,10,[14][15][16][17][18] and books [11,13] that have appeared.…”

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confidence: 99%

Book Review: Algebraic curves over finite fields

Hirschfeld¹

1992

Bull. Amer. Math. Soc.

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Generalized Reed - Solomon codes from algebraic geometry

Cited by 58 publications

References 7 publications

A simple combinatorial treatment of constructions and threshold gaps of ramp schemes

A simple combinatorial treatment of constructions and threshold gaps of ramp schemes

A Low Complexity Algorithm and Architecture for Systematic Encoding of Hermitian Codes

Book Review: Algebraic curves over finite fields

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