Pless, V.S., Hu#man, W.C. (Eds.): Handbook of Coding Theory (2 volumes). Elsevier (1998) Home/Search Document Not in Database Summary Related Articles Check |
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Linear Transformations on Codes - Glynn, Gulliver, Gupta (Correct)
....in Section 3. Section 4 defines the concatenated transformations. Section 5 investigates applications of these transformations. The last section finishes with some conclusions. 2 Preliminaries and Notations We list the families of codes which we will consider here. The standard notation is from [4]. Note that the list starts from (2) because there is no field of order 1. 2) Binary linear codes: F = F 2 = 1 , with standard inner product (x, y) xy, a subspace of F 2 . 3) Ternary linear codes: F = F 3 = 1, 2 , x, y) xy, 3 . Note that for families (2) and (3) an additive ....
....taken from the generator matrix of a q ary simplex code of dimension n. Also, A 1 is the identity matrix of order n. The next theorem tells us about the e#ect the j weight irreducible transformation on the Hamming weights of a code of length n. The q ary Krawtchouk polynomials are defined in [4]. For j = 0, 1, 2, the Krawtchouk polynomials K j (x) are defined by K j (x; n, q) K j (x) where : x(x (x k 1) k , x R) Theorem 1 Let c be a codeword of weight i. Then the weight of a transformed codeword in # is K j (i) Proof. Let w ....
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V. Pless and W. C. Hu#man (Eds.) The Handbook of Coding Theory. North-Holland, New York, 1998.
Gröbner Basis Solutions of Constrained Interpolation Problems - O'Keeffe, Fitzpatrick (2001) (Correct)
....matrices, which multiplies the determinant by a constant or a constant multiple of x s . 6 List decoding, soft decision decoding In this section we apply our general techniques to speci c problems for error correcting codes. The basic theory can be found in a number of references such as [14, 17, 18]. Throughout the section we will be dealing with 2 variable poynomials only, so we change our notation slightly to t with that established in the literature: henceforth n refers to the number of congruences in (1) and (2) so replaces p) When the number of errors in a received word exceeds half ....
V.S. Pless, W.C. Hu man (eds), Handbook of Coding Theory, Elsevier, Amsterdam, 1998.
Coding Theory: Tutorial Survey - Sudan (Correct)
....storage of information. This, in turn, became the primary motivator for much research in the theory of error correcting codes. As a result, today it is very common to see articles that ascribe origins of the entire theory to Shannon s work, cf. 49, Chapter 1] 96] The Handbook on Coding Theory [49], for instance, introduces Shannon s work on the rst page and waits for about ten pages before mentioning Hamming s work. 1.1 Basic definitions We now move on to some of the basic notions of coding theory. To de ne codes, messages, and other such notions, let us follow a message on its path ....
.... text of MacWilliams and Sloane [63] the concise text of van Lint on algebraic coding theory [59] the out ofprint, but highly recommended, book by Blahut [15] which is an excellent source for some of the algorithmic works, and the highly detailed (and not so handy) handbook of coding theory [49]. Acknowledgments Many thanks to Venkatesan Guruswami for many conversations, and pointers to the early history. ....
C. Hu man and V. Pless. Handbook of Coding Theory, volumes 1 & 2. Elsevier Sciences, 1998.
On Single-Deletion-Correcting Codes - Sloane (2001) (4 citations) (Correct)
....This paper considers the very simplest family of such codes, binary block codes capable of correcting single deletions. Even for these codes there remain several apparently unsolved problems. It is surprising, but these codes do not appear to be surveyed in any of the usual references ( MS77] PH98] etc. This paper is a first attempt at such a survey. It will be posted on the author s home page [SL00] and will be updated as appropriate. It is hoped that the problems mentioned here will either soon be solved or will turn out to be already solved. Proofs are given of a number of results, ....
V. S. Pless and W. C. Hu#man, Handbook of Coding Theory, NorthHolland, Amsterdam, 1998.
On Polynomial Invariants of Linear Codes, Matroids, and Finite.. - Barg (1999) (Correct)
....We conclude by returning to codes and showing that certain generalizations of the weight polynomial fall naturally in the general pattern of the paper. Coding theoretic concepts are perhaps the least standard of all the material in the paper. General sources for coding theory are the books [37] [39]. Graph theoretic codes were introduced in [23] 22] They are relatively well understood from the coding point of view; see a summary in [29] Relevant applications of the Tutte polynomial are covered in [13] 47] All the necessary information on interaction models is contained in [47] or, on ....
V. Pless and W. C. Huffman (eds.), Handbook of coding theory, vol. 1,2, Elsevier Science, Amsterdam, 1998, 2169pp.
Efficient FPGA Implementations and Cryptanalysis of.. - Trinca (2006) (Correct)
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Pless, V.S., Hu#man, W.C. (Eds.): Handbook of Coding Theory (2 volumes). Elsevier (1998)
Bounds on Codes Derived By Counting Components in - Varshamov Graphs Katie (Correct)
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V. Pless, W.C. Hu#man (eds), Handbook of Coding Theory, Elsevier Science, Amsterdam, 1998.
Enumeration Of Inequivalent Irreducible Goppa Codes - John Ryan And (Correct)
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Pless, V.S. and Hu#man, W.C., eds., Handbook on Coding Theory, Elsevier Science, 1998.
Sequential and Parallel Cascaded Convolutional Encryption with.. - Trinca (2006) (Correct)
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Pless, V.S., Hu#man, W.C. (Eds.): Handbook of Coding Theory (2 volumes). Elsevier (1998)
A Polynomial Algorithm for Codes Based on Directed Graphs - Kelarev School Of (Correct)
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Pless, V. S., Hu#man, W. C. & Brualdi, R. A., eds., (1998), Handbook of Coding Theory, Elsevier.
Enumeration Of Inequivalent Irreducible Goppa Codes - John Ryan And (2004) (Correct)
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Pless, V.S. and Hu#man, W.C., eds., Handbook on Coding Theory, Elsevier Science, 1998.
Lecturer: Madhu Sudan Scribe: Ryan O'Donnell - Error Correcting Codes (Correct)
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Vera S. Pless and W. Cary Hu man (Eds.). Handbook of Coding Theory (2 Volumes). Elsevier, 1998.
Using the Trace Operator to Repair the Polynomial.. - Augot, Finiasz, Loidreau (2003) (3 citations) (Correct)
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V. S. Pless and W. C. Human, editors. Handbook of Coding Theory. Elsevier Science B.V., 1998.
New covering radius of Reed-Muller codes for t-resilient.. - Kurosawa, Iwata.. (2002) (1 citation) (Correct)
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V.S.Pless and W.C.Hu man, editors, \Handbook of Coding Theory", North Holland, 1998. 21
List Decoding: Algorithms and Applications - Sudan (2000) (7 citations) (Correct)
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Vera Pless, W. Cary Huffman, and Richard A. Brualdi (Eds.). Handbook of Coding Theory, North-Holland, 1998.
SIGACT News Complexity Theory Column 25 - Lane Hemaspaandra Dept (Correct)
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Vera Pless, W. Cary Huffman, and Richard A. Brualdi (Eds.). Handbook of Coding Theory, North-Holland, 1998.
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