By D J. Baylis
Assuming little prior mathematical wisdom, errors Correcting Codes presents a legitimate creation to key components of the topic. issues were selected for his or her value and functional value, which Baylis demonstrates in a rigorous yet mild mathematical style.
Coverage contains optimum codes; linear and non-linear codes; basic innovations of deciphering mistakes and erasures; blunders detection; syndrome interpreting, and masses extra. blunders Correcting Codes includes not just instantly maths, but in addition routines on extra investigational challenge fixing. Chapters on quantity thought and polynomial algebra are integrated to help linear codes and cyclic codes, and an in depth reminder of correct issues in linear algebra is given.
Exercises are positioned in the major physique of the textual content to inspire energetic participation through the reader, with finished recommendations provided.
Error Correcting Codes will attract undergraduate scholars in natural and utilized mathematical fields, software program engineering, communications engineering, machine technological know-how and data expertise, and to enterprises with big study and improvement in these parts.
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Additional info for Error-correcting Codes: A mathematical introduction
Y2 = 999 has no 27. If ais composite and a 2: 6 prove that al(a - I)! 28. Are the following true or false? Prove the true statements and provide a counter example for the false ones (a and b are positive integers and p is prime): (a) (b) (c) (d) ifgcd(a,b) =pthen gcd(a 2,bp) =p2; if gcd(a,p2) = p and gcd(b,p2) = p2 then gcd(ab,p4) = p3 ; if gcd(a, b) = p then gcd(a 2 , ab) = p2 ; if a 2 + b2 = p2 then gcd(a, b) = 1. 47 Exercises for Chapter 3 29. 1464463 14108963 72 X 11 2 11 2 so gcd(1464463, 14108963) X 13 X X = 11 2 X 19 17 X 19 193 = 2299.
It was first shown to me by Ray Hill . It is a 'number guessing' game for two players, Gwen the great guesser and Llew the limited liar. Gwen asks Llew to choose a number between zero and fifteen inclusive but to keep it to hirnself. She then asks hirn seven questions for which he has a furt her choice: either answer them all truthfully or answer six correctly but lie in reply to the other. He does not have to reveal whether he is lying at any point. From the answers Gwen is able to say what the number is, whether he has lied, and if so, in reply to which question.
3), = gcd(372, 288) 84 ... (4), gcd(288, 84) 36 ... (5), = gcd(84, 36) (6), = gcd(36, 12) = gcd(12, 0) 0 ... (7), = [TI] ... =[ill The proeess is terminated onee a zero remainder is reaehed, in this ease after seven divisions. Clearly there is not hing special ab out the numbers 3840 and 1404, so we eould start with any pair of integers and the result would be that their ged is the last non-zero remainder. ' WeIl, suppose the sequenee of remainders is rl, r2, r3, .... To obtain r2 we do a division by rl so r2 < rl' To obtain r3 we do a division by r2 so r3 < r2, ...
Error-correcting Codes: A mathematical introduction by D J. Baylis