By Jaques Calmet

ISBN-10: 3540167765

ISBN-13: 9783540167761

ISBN-10: 3540398554

ISBN-13: 9783540398554

**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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**Additional info for Algebraic Algorithms and Error-Correcting Codes: 3rd International Conference, AAECC-3 Grenoble, France, July 15–19, 1985 Proceedings**

**Example text**

Q - i . binary The f o l l o w i n g Further, In [6], code with t h e s e theorem genera- case. a non-trivial positive 1 C has which p = n / (e + I) strongly integer Then C has e the and tactical prime parameters of length (2), the sphere packing condition e+1 n )i n e+l (I)(q-1 + (e+l)(q-l) = ~ {e,e+l}- power q) with of a punc- reads n+1. i ( i )(q-S) i=0 is the sphere codes q- be cor- codewords code. n+q i e = q" ~ IUi i=0 This n q (with = where e e JN Golay C F code and e = 2 correcting Pe,e to the q-ary Let correcting ~e,e punctured this r e s u l t if coordinate for as C), {e,e÷l}-error two Then and by d e l e t i n g with as C.

With D i s t i n c t P r o t e c t i v e 32 (1983), 379 - 396. North-Holland, Monteron, Rev. H. Paris S~r A - E, and S t e i n e r - 200. Radii; Atti Sem. Mat. Modena, 7. 12. 26 C v e t k o v i ~ , J. H. van Lint: An E l e m e n t a r y Proof of Lloyd's Theorem; N e d e r l . Akad. W e t e n s c h . Indag. M a t h . , 80 (1977), 6 - 10. Fis. 11. (2), G. Cohen, B. Montaron: Empilements p a r f a i t s de boules dens los espaces vectoriels 288 (1979), no 11, I0. Soc. 234. Amsterdam Tactical Springer, Theory; Theory - New Codes; of York ManuBerlin - Error-Correcting 1977.

Shows t h a t P2,1 ~1,2 codes extended IC I = 2 n'm-1 code (extended) and P(m) and and codes of length polynomial Theorems m is an even integer. correcting is the c h a r a c t e r - correcting correcting We p u t clear e-error cherecteristic C = Hext(m) where ~1 = 2 n-2m pl , i packed is the [-q of the above t h e o r e m (e+l)-error in C is 4, 2-error 2 n-2m The z e r o s Classification n = 2m , mum d i s t a n c e Q(x) of u n i f o r m l y X = 0 . Ki(x,n,q) polynomials. The p o l y n o m i a l polynomial n with % i=0 by Theorem 2 .

### Algebraic Algorithms and Error-Correcting Codes: 3rd International Conference, AAECC-3 Grenoble, France, July 15–19, 1985 Proceedings by Jaques Calmet

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