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

By N.J.A. Sloane

Show description

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

Similar computer science books

Logic for Computer Science and Artificial Intelligence (ISTE)

Common sense and its parts (propositional, first-order, non-classical) play a key function in laptop technological know-how and synthetic Intelligence. whereas a large number of details exists scattered all through quite a few media (books, magazine articles, webpages, and so on. ), the diffuse nature of those resources is challenging and common sense as an issue merits from a unified technique.

Computation and Storage in the Cloud: Understanding the Trade-Offs

Computation and garage within the Cloud is the 1st finished and systematic paintings investigating the problem of computation and garage trade-off within the cloud in an effort to decrease the general software fee. medical functions tend to be computation and knowledge extensive, the place complicated computation projects take many years for execution and the generated datasets are usually terabytes or petabytes in measurement.

Coding the Matrix: Linear Algebra through Applications to Computer Science

An enticing advent to vectors and matrices and the algorithms that function on them, meant for the scholar who is aware how one can software. Mathematical suggestions and computational difficulties are prompted via purposes in computing device technology. The reader learns via doing, writing courses to enforce the mathematical innovations and utilizing them to hold out projects and discover the purposes.

Genetic Programming Theory and Practice IV (Genetic and Evolutionary Computation)

Genetic Programming thought and perform IV used to be constructed from the fourth workshop on the college of Michigan’s middle for the research of complicated structures to facilitate the trade of principles and knowledge with regards to the speedily advancing box of Genetic Programming (GP). Contributions from the key foreign researchers and practitioners within the GP enviornment study the similarities and variations among theoretical and empirical effects on real-world difficulties.

Additional info for A Short Course on Error Correcting Codes

Example text

U. I i =1 . S1 + bJ. wt(B1 s1 ) ~ 3, = BT ST • , ••• ,e 1 ~ = 1, so for some j, 1 ~j ~ 12, Thus the decoding can be done by computing the weights of the 26 vectors (1 ~ j ~12), B1 S 1 , B1 S1 + bj (1 ~ j ~ 12). Example: S=11100 ... 0, wt(S) = 3, socaseI applies. S1 , S = S1 +bj u 1 + u2 + u 3 , so e = 11100 ••• 0. (3. 6. 2) Decoding Metbad II (Goethals [ 6 7 ] ) This is a clever threshold decoding scheme, using the properties of the designs associated with the code. 4 ), any set of codewords can be used as parity checks for the code.

Use Gleason's theorem to obtain the weight distribution of the code. 4) Example 3 Let ~ be a self-dual code of length n = 8j in which all weights are divisible by 4. What is its greatest possible minimum distance? By Th. 1) (ii), with m = [n/24], w= E · -3k k m e2 , ~c;2 k=O which contains m + 1 parameters ~. 5) § § 4 The Theorems of MacWilliams and Gleason 54 which corresponds to a hypothetical code with minimum distance at least 4m + 4. Of course if it should turn out that A 4m+ 4 =0, the minimum distance would be greater than 4m + 4.

1) Example 1 A self-dual code oflength 12 contains no codewords ofweight 2. What is its weight enumerator W? By Th. 2) Example 2 Is there a self-dual code oflength 32 with"minimum distance 10? By Th. 1) (i), its weight enumerator W has the form Equating coefficients we find that a1 , ... ,a 5 are uniquely determined and that W = x32 + 4960x22 yto - 34 72x'1D y12 + Since a weight enumerator cannot have a negative coefficient, no such code exists. 3) Exercise Take all the codewords in the [24,12,8] extended Golay code which begins either with 00...

Download PDF sample

Rated 4.39 of 5 – based on 50 votes