I. Honkala and A. Tietavainen: Codes and number theory. In Handbook of Coding Theory (Eds. R. A. Brualdi, W. C. Huffman and V. S. Pless), to appear.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....with designed distance 2r 1. Define X , the corresponding set of sequences, as in the discussion above. By (8.3) and Theorem 4.1, #(X) 1 (2r Gamma 2)q #(x) can be estimated by using Vinogradov s method. By Theorem 4.3, the sum (8.4) can be upper bounded by (2r Gamma 1)q . Thus ( 20] [15]) #(X) 2r Gamma 1)q 3) Small Kasami sets of sequences. Let q = 2 2r and 2 F q n F 2 r and choose P = fbx ax 2 r 1 jb 2 F q ; a 2 F 2 r g. The code C(P ) is cyclic because f(flx) 2 P for all f(x) 2 P . Denote f(x) bx ax . The case a = 0 is trivial. If a 6= 0 ....

I. Honkala and A. Tietavainen: Codes and number theory. In Handbook of Coding Theory (Eds. R. A. Brualdi, W. C. Huffman and V. S. Pless), to appear.

....distance 2r 1. Define X , the corresponding set of sequences, as in the discussion above. By (8.3) and Theorem 4.1, #(X) 1 (2r Gamma 2)q 1=2 : #(x) can be estimated by using Vinogradov s method. By Theorem 4.3, the sum (8.4) can be upper bounded by (2r Gamma 1)q 1=2 . Thus ( 20] [15]) #(X) 2r Gamma 1)q 1=2 (L(q Gamma 1) 1) 3) Small Kasami sets of sequences. Let q = 2 2r and 2 F q n F 2 r and choose P = fbx ax 2 r 1 jb 2 F q ; a 2 F 2 r g. The code C(P ) is cyclic because f(flx) 2 P for all f(x) 2 P . Denote f(x) bx ax 2 r 1 . The case a = 0 is ....

I. Honkala and A. Tietavainen: Codes and number theory. In Handbook of Coding Theory (Eds. R. A. Brualdi, W. C. Huffman and V. S. Pless), to appear.

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