J. Lint and G. van der Geer, Introduction to coding theory and algebraic geometry, Birkhauser, Boston, 1988. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Which Linear Codes Are Algebraic-Geometric? - Pellikaan, Shen, van Wee (1991) (Correct)
....exciting results have been achieved using Goppa s construction of linear codes from algebraic curves over finite fields, both by algebraic geometrists and coding theorists. Because of the difficulty of the subject, several explanatory papers and text books have appeared, see for instance [9] or [16]. In this paper we investigate which linear codes can be constructed by Goppa s method. It turns out that it makes sense to distinguish between three types of codes, according to the degree of the divisor used in the construction. For more details, see Section II (Definition 2) All authors are ....
....PO Box 513, 5600 MB Eindhoven, The Netherlands. This research was partially supported by the Netherlands organization for scientific research (NWO) 1 Although this paper is quite self contained, a certain knowledge of algebraic geometry is taken for granted. For this, we refer to [2] 4] 11] [16] or [22] For coding theory, see [15] 16] or [17] Outline of the paper In Section II we define weakly algebraic geometric (WAG) algebraic geometric (AG) and strongly algebraic geometric (SAG) codes (Definition 2) The class of SAG codes is a proper subset of the class of AG codes, and the ....
[Article contains additional citation context not shown here]
J.H. van Lint and G. van der Geer, Introduction to coding theory and algebraic geometry. DMV Seminar 12. Birkhauser Verlag, Basel Boston Berlin, 1988.
Algebraic Geometric Codes Over Rings - Walker (1996) (1 citation) (Correct)
....as in [5] 10] and [8] 2. Linear Codes over Finite Fields The purpose of this short section is to catalog some basic definitions and results about linear codes over finite fields, including algebraic geometric codes over finite fields. The references for this section are [9] 11] 13] and [15]. We begin with some definitions. A code C of length n over the finite field F q is a subset of the vector space F n q . If C is actually a subspace, it is called a linear code and its dimension k is its dimension as a F q vector space. Elements of C are called codewords. The Hamming distance ....
....: f # L(D) ALGEBRAIC GEOMETRIC CODES OVER RINGS 3 The second algebraic geometric code associated to X , P , and D is given by C# = C# (X, P , D) res P1 (#) res Pn (#) # # ## P D) We summarize the properties of CL and C# in a theorem, due to Goppa. See [11] 13] or [15] for the proof. Theorem 2.1. Let X, P and D be as above, and suppose that 0 # deg D n = P . Then 1. CL is a linear code of length n. The dimension kL and minimum distance dL of CL satisfy kL # deg D 1 g, dL # n deg D. 2. C# is a linear code of length n. Its dimension k# and ....
J. H. van Lint and G. van der Geer. Introduction to Coding Theory and Algebraic Geometry. Birkhauser, Basel, 1988.
Remarks on Codes From Modular Curves: - Maple Applications David (Correct)
No context found.
J. Lint and G. van der Geer, Introduction to coding theory and algebraic geometry, Birkhauser, Boston, 1988.
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC