University of Illinois Fall 2005 ECE 556: Second MidSemester Exam Thursday November 17, 2005, 8:30 a.m. – 9:50 a.m. This is a open-text open-handwritten-notes examination. No printed materials other than the textbook and Problem Sets and Solutions distributed in class are permitted. Calculators, laptop computers, PDAs, iPods, cellphones, e-mail pagers, etc. are neither needed nor permitted. This Examination contains three problems 1 . Let m denote an even integer, α a primitive element of GF(2 m ), and β = α 1+2 m/ 2 . ( a ) Show that β is a primitive element of the subﬁeld GF(2 m/ 2 ). ( b ) What is the BCH bound on the minimum distance of the low-rate binary cyclic code of length 2 m-1 whose parity-check polynomial h ( x ) is M α ( x ) M β ( x )? Here, as usual, M α ( x ) and M β ( x ) are the minimal polynomials of α and β over GF(2). 2 . Let α denote a primitive element of GF(2 5 ) with minimal polynomial x 5 + x 2 +1, and consider a 5-error-correcting binary BCH code of length 31. Suppose that the syndrome polynomial
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This note was uploaded on 02/08/2012 for the course ECE 556 taught by Professor Milenkovic,o during the Fall '08 term at University of Illinois, Urbana Champaign.