Titlebook: Coding Theory; Jacobus H. Lint Book 1973Latest edition Springer-Verlag Berlin Heidelberg 1973 Finite.algebra.coding.coding theory.error-co

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Introduction,ctice this is not the case. . is added to the information and as a result . are introduced by the channel. For example in telephone conversations there is cross-talk, thermal noise, impulsive switching noise, sometimes lightning causes noise; in radio we have static; magnetic tapes sometimes have the wrong digits after storage etc.

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0075-8434 t the California Institute of Technology. The students who took the course were mathematics seniors and graduate students. Therefore a thorough knowledge of algebra. (a. o. linear algebra, theory of finite fields, characters of abelian groups) and also probability theory were assumed. After introduc

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Nani G. Bhowmik,J. Rodger Adamsis the residue class ring R mod S, i.e. (GF(q)[x] mod ({x.-1},+, ). The elements of this ring can be represented by polynomials of degree < n with coefficients in GF(q). The additive group of R/S is isomorphic to .. An isomorphism is given by associating the vector . = (a.,a., ... ,a.) with the polynomial a. + a.x + ... + a.x..

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純樸

Cyclic codes,is the residue class ring R mod S, i.e. (GF(q)[x] mod ({x.-1},+, ). The elements of this ring can be represented by polynomials of degree < n with coefficients in GF(q). The additive group of R/S is isomorphic to .. An isomorphism is given by associating the vector . = (a.,a., ... ,a.) with the polynomial a. + a.x + ... + a.x..

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Perfect codes, the first nonzero entry in each column is 1. Since no linear combination of two columns can be . we see that H is the parity check matrix of a linear (n,k) code over GF(q) with minimum distance 3. Because q.{1 + n(q-1)} = q. = q. the code is perfect.

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Book 1973Latest editionerm these two topics would have been chosen. Although the material for this course came from many sources there are three which contributed heavily and which were used as suggested reading material for the students. These are W. W. Peterson‘s Error-Correcting Codes ?(15]), E. R. Berlekamp‘s Algebrai

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monochromatic

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Rodent

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