New PDF release: A Short Course on Error Correcting Codes

By N.J.A. Sloane

ISBN-10: 3211813039

ISBN-13: 9783211813034

ISBN-10: 3709128641

ISBN-13: 9783709128640

Show description

Read Online or Download A Short Course on Error Correcting Codes PDF

Similar computer science books

Download e-book for iPad: Numerical Partial Differential Equations: Finite Difference by J. W. Thomas

Of the numerous assorted methods to fixing partial differential equations numerically, this publication reviews distinction equipment. Written for the start graduate scholar in utilized arithmetic and engineering, this article bargains a way of popping out of a direction with a good number of equipment that supply either theoretical wisdom and numerical event.

Download e-book for iPad: GPU PRO 3: Advanced Rendering Techniques by Wolfgang Engel

GPU Pro<SUP>3</SUP>, the 3rd quantity within the GPU seasoned publication sequence, deals functional information and strategies for growing real-time pictures which are priceless to rookies and professional online game and pix programmers alike.

Section editors Wolfgang Engel, Christopher Oat, Carsten Dachsbacher, Wessam Bahnassi, and Sebastien St-Laurent have once more introduced jointly a superior number of state of the art thoughts for complicated GPU programming. With contributions by way of greater than 50 specialists, GPU Pro<SUP>3</SUP>: complex Rendering ideas covers battle-tested counsel and methods for growing attention-grabbing geometry, reasonable shading, real-time international illumination, and top of the range shadows, for optimizing 3D engines, and for benefiting from the complex strength of the GPGPU.

Sample courses and resource code can be found for obtain at the book's CRC Press internet page.

Download e-book for iPad: Machine Musicianship by Robert Rowe

Musicians commence formal education by way of buying a physique of musical suggestions generally known as musicianship. those suggestions underlie the musical talents of listening, functionality, and composition. Like people, computing device track courses can reap the benefits of a scientific beginning of musical wisdom. This ebook explores the expertise of enforcing musical tactics equivalent to segmentation, development processing, and interactive improvisation in machine courses.

New PDF release: Computers, Chess and Long-Range Planning

Mihail Moiseevich Botvinnik is an electric engineer by way of occupation; in the course of global struggle II he headed a high-tension laboratory within the Urals and was once adorned by way of the USSR for his accomplishments. at the moment, he's the pinnacle of the alternating-current desktop laboratory on the Moscow Institute of strength Engineering.

Additional resources for A Short Course on Error Correcting Codes

Example text

4. 10) is a special case of a theorem of Perron [ 78] . 14) has been studied by Assmus and Mattsou [59], [60] , Goethals [67], and many others. Pless [ 79] has shown that the Golay code is unique. 17 are taken from Conway[66]. 16) is from Goethals [ 6 7] . 6) Berlekamp [ 62 ] also considers which error patterns of weight 4 can be corrected. F. , (1966), Perfeet Codes and The Mathieu Groups, Arch. Math. 17:121-135. F. , (1969), New 5-Designs, JCT 6:122-151. R. (1971), Coding Theory and the Mathieu Groups, IC 18:40-64.

4) The code ~ was first discovered by Golay [ 25] , [ 26] . 1) was found by Paige [77 ], and later rediscovered by Leech [71] and Karlin [ 69]. The discussion given here follows Karlin and MacWilliams [ 70 ] - see this reference for a proof of Theorem (3. 4). Golay gave another perfect code in [ 25], an [ 11,6,5] code over the field GF(3). It can be defined by the generator matrix G = [ 16 lll;ll J where A is a circulant with first row (0,1,-1,-1,1) (van Lint [2], p. 103). 1 0. In 1967 Leech [ 72 ] used the Golay code to construct a very dense sphere packing in 24-dimensional Euclidean space.

I yi Finding the weight enumerator of a large code is m general very difficult. 3 Extending. 1) Lemma Let c be any (n,M,d) code with d odd. By adding a 0 at the end of each codeward of even weight, and a 1 at the end of each codeward of odd weight, we obtain a new (n + 1,M,d +1) code c'. Extending a Code 31 Proof. 3 ), the distance between any two vectors of c' is even. The minimum distance cannot be less than d (which is odd), so must be d + 1. D. 5) we obtain the (8,16,4) extended Hamming code.

Download PDF sample

A Short Course on Error Correcting Codes by N.J.A. Sloane


by David
4.2

Rated 4.40 of 5 – based on 26 votes