March 28, 2017

Download An Introduction to Algebraic and Combinatorial Coding Theory by Ian F. Blake PDF

By Ian F. Blake

Show description

Read or Download An Introduction to Algebraic and Combinatorial Coding Theory PDF

Similar combinatorics books


The articles accrued listed here are the texts of the invited lectures given on the 8th British Combinatorial convention held at college collage, Swansea. The contributions replicate the scope and breadth of program of combinatorics, and are updated studies through mathematicians engaged in present examine.

Higher Dimensional Varieties and Rational Points

Exploring the connections among mathematics and geometric homes of algebraic forms has been the thing of a lot fruitful learn for a very long time, specially on the subject of curves. the purpose of the summer time tuition and convention on "Higher Dimensional forms and Rational issues" held in Budapest, Hungary in the course of September 2001 was once to compile scholars and specialists from the mathematics and geometric facets of algebraic geometry with a view to get a greater figuring out of the present difficulties, interactions and advances in greater measurement.

The Probabilistic Method (Wiley-Interscience Series in Discrete Mathematics and Optimization)

I take place to like learning likelihood idea and the probabilistic approach and this can be the publication I come to time and time back. it's good prepared and gives nice, easy, insightful reasons. although, its major power is its wealth of lovely (fairly lately) effects (in diversified fields) which exhibit the strategy coming to existence.

The Grassmannian Variety: Geometric and Representation-Theoretic Aspects

This publication provides a finished remedy of the Grassmannian forms and their Schubert subvarieties, targeting the geometric and representation-theoretic facets of Grassmannian types. study of Grassmannian forms is situated on the crossroads of commutative algebra, algebraic geometry, illustration idea, and combinatorics.

Extra info for An Introduction to Algebraic and Combinatorial Coding Theory

Sample text

Delsarte (1973a) investigates codes over Abelian groups. Again, with the proper definition of a dual code, the MacWilliams identities still hold. There are also interesting relationships between Krawtchouk polynomials and weight enumeration [see MacWilliams et al. (1972c) and Delsarte (1973a)] and some of these are mentioned in Exercise 22. If the weight enumerator B(z) of <é>L is known, then the above theorem gives a set of n + 1 linear equations in the n + 1 unknowns A{,, i = 0, . . , n. In a practical situation it is possible that not all of the coefficients of B(z) may be known and in this case the so-called power moment identities of Pless (1963) may be important.

Together with the previous equations they are called the Newton identities. Apply these equations and the previous ones to the polynomial Ax)=tf-x which, of course, splits over GF(q) and has all the elements of GF(q) as zeros. l = — 1, we conclude that P{ = 0 for 0 < / < q — 1 and Pq_l = q — 1. 5 Let 0,, / > 0, denote the sum of the /th powers of the elements of GF(q). Then 0=[q-\ ' \0 if ( ? - D | / otherwise There is a fascinating literature on the study of polynomials over a finite field but it would be inappropriate to review it here.

Notice that for each set k\n. This process partitions elements into disjoint subsets. Elements of GF(q) are in sets of cardinality one. All other elements are in sets with more than one element. This partition of elements of GF(qn) induces a partition of the integers 0, 1, . . , qn — 2 where each set of integers comprises the exponents of the elements in a set in the partition of GF(qn). -i)(0 = '9niod(? n - 1) This mapping partitions the integers into disjoint sets which we shall denote by st and, again, the cardinality of each such set is a divisor of n.

Download PDF sample

Rated 4.52 of 5 – based on 42 votes