By Jaques Calmet
Read or Download Algebraic Algorithms and Error-Correcting Codes: 3rd International Conference, AAECC-3 Grenoble, France, July 15–19, 1985 Proceedings PDF
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Extra resources for Algebraic Algorithms and Error-Correcting Codes: 3rd International Conference, AAECC-3 Grenoble, France, July 15–19, 1985 Proceedings
A. Z i n o v j e v , N~ V. S e m a k o v : I n t e r r e l a t i o n of Preparata and Hamming Codes and E x t e n s i o n o f Hamming Codes t o New D o u b l e - E r r o r - C o r r e c t i n g Codes; Proc. 2nd Int. Symp. Inform. Theory ( A k a d ~ m i a i K i a d B , B u d a p e s t , 1 9 7 3 ) , 257 - 2 6 3 . INTEGER PROGRAMMING APPLIED TO EISENVECTOR COMPUTATION IN A CLASS OF MARKOV PROCESSES Andre OISEL CI I-HonmywelI BULL, 78340 LES CLAYES-S-BOIS , France ABSTRACT I The encoding of d a t a i n a number o f r e c o r d i n g and t r a n s m i s s i o n d e v i c e s can be m o d e l i z e d by a Markov p r o c e s s .
Q is P2 => P3 ~-irreducible) is t r u e for every polynomial of height less to k-1. Let S I ~+ R I, a n d One can prove -I- The The 0 the height h(Q) lynomial property and S~ P2 or equal ~-irreducible. + y ( F I , . . , F r) => S ~+ 0 PI => by + F I is following S 6 we proceed + 3XY 3 + X Y 2 + XY + y2 + y2 is 3. pl progf¥ of t h e ~~irreducible. the same notations steps We will Q ~+ Q' The polynomial Property several reducible. $I ~+ R 2 b e that two previous the the fact By induction (and a l s o RI are following simplify that SPOL(Fi,Fj)~+0 case, which two derivations -2,- In t h e o t h e r polynomials derivations R I and R 2 can be derived T, c o n s i d e r i n g one uses two one can directly R 2) h a s equal.
I Example 7 Q - 8 x~ I-iI... X nin. e. xJn-inn Fj, this d e r i v a t i o n (ordered with a simplification) FI= which, a polynomial by : Q ~ by l e x i c o g r p h i c a l without term Q'. ordering), 2X2Y 3 + X2Y + 3XY 2 + Y, 2X3Y + XY z + Y. S u p p o s e from Q, let and Q is 4X~Y 2 + 3X2Y 4 + XY. One has Q ~+ Q', with Q' = Q - 2 XY F 2 = 3X2Y ~ - 2X2Y 3 - 2XY 2 + XY 51 Definition 5 Suppose we obtain Suppose Q' of Q ~+ Q') : Q' The number Example 8 Q' after is n o l o n g e r of With is s a i d to b e steps the is c a l l e d '~derivation" denote Q ~+Q' (in place length as of t h e in e x a m p l e "derivation".
Algebraic Algorithms and Error-Correcting Codes: 3rd International Conference, AAECC-3 Grenoble, France, July 15–19, 1985 Proceedings by Jaques Calmet