By Jaques Calmet
Read Online 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
T has non n e g a t i v e c o o r d i n a t e s . As a consequence, no c o o r d i n a t e o f V~ can be h i g h e r than t h e c o r r e s p o n d i n g c o o r d i n a t e o f M . ~ . Hence W~ i s bounded by M . ~ . , and UI+ ! i s bounded b y ~ . CONCLUDING PROOF : One consequence o f LEMMAs 1 & 4 i s t h a t ends a f t e r a l i m i t e d number o f s t e p s . From Lemma 3 : U ~ / I 5) e = U~ . U~ ; COMPLEXITY the process In t h a t case : W~ = U ; . T and W~ = M . U ~ I U/~ i s t h e e x p e c t e d E i g e n v e c t o r .
Is over sum runs over manifolds (s) [Y]). : and then (the d i r e c t in ~ and we can conclude. (the i n t e r s e c t i o n e Q' (~,8), algebraic ((X 2 + y (I+PO(~,8)), and = (1), X,Y]). morphism = N Q' (y,~) c) A g e n e r a t o r = of (in = ~(Q(~,8)), I and W2(a,Y) (mod I), and we can conclude. canonical b) A = @ Q' (~,B) in I. p~ Let ~ b e t h e a) A = Q' (~,8) not proof Let Q' (~,S) Q' (a,S) by where + k2W~, k p~ (k+1) W2 - ~1W2 fined ~, that I = W 2 W ~ + 8W I ((W2(~,Y) , W~(e,Y)) I = ~IW2 Remark of ~ over W2(X,Y)), ]Fq(a).
1 or of the punctured t e r n a r y Golay code. References 1. A. Bremner, R. Calderbank: Two-Weight Ternary Codes and the Equa- 2. R. Calderbank: On Uniformly Packed [ n , n - k , 4 ] Codes over GF(q) and y2=4x3a+13;J. tion a Class (1982), 3. Numb. Theory of Caps in P G ( k - l , q ) ; 365 - 3 8 4 . 16 (1983), 2 1 2 - , J. London Math. b i n a i r e s ; c. R. A 579 - A 582. Acad. Sci. 4. G. Cohen, P. Frankl: On G e n e r a l i z e d P e r f e c t Codes Systems; Ann. D i s c r e t e M a t h . , 18 (1983), 197 5.
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