A034190 Number of binary codes of length 5 with n words.
1, 1, 5, 10, 47, 131, 472, 1326, 3779, 9013, 19963, 38073, 65664, 98804, 133576, 158658, 169112, 158658, 133576, 98804, 65664, 38073, 19963, 9013, 3779, 1326, 472, 131, 47, 10, 5, 1, 1
Offset: 0
References
- W. Y. C. Chen, Induced cycle structures of the hyperoctahedral group. SIAM J. Disc. Math. 6 (1993), 353-362.
- H. Fripertinger, Enumeration, construction and random generation of block codes, Designs, Codes, Crypt., 14 (1998), 213-219.
- R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1979.
Links
- H. Fripertinger, Isometry Classes of Codes
Crossrefs
Programs
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Mathematica
(* From Robert A. Russell, May 08 2007: (Start) *) P[ n_Integer ]:=P[ n ]=P[ n,n ];P[ n_Integer,_ ]:={}/;(n<0);(* partitions *) P[ 0, ]:={{}};P[ n_Integer,1 ]:={Table[ 1,{n} ]};P[ ,0 ]:={};(*S.S. Skiena*) P[ n_Integer,m_Integer ]:=Join[ Map[ (Prepend[ #,m ])&,P[ n-m,m ] ],P[ n,m-1 ] ]; AC[ d_Integer ]:=Module[ {C,M,p}, (* from W.Y.C. Chen algorithm *) M[ p_List ]:=Plus@@p!/(Times@@p Times@@(Length/@Split[ p ]!)); C[ p_List,q_List ]:=Module[ {r,m,k,x},r=If[ 0==Length[ q ],1,2 2^ IntegerExponent[ LCM@@q,2 ] ];m=LCM@@Join[ p/GCD[ r,p ],q/GCD[ r,q ] ]; CoefficientList[ Expand[ Product[ (1+x^(k r))^((Plus@@Map[ MoebiusMu[ k/# ] 2^Plus@@GCD[# r,Join[ p,q ] ]&,Divisors[ k ] ])/(k r)),{k,1,m} ] ],x ] ]; Sum[ Binomial[ d,p ]Plus@@Plus@@Outer[ M[ #1 ]M[ #2 ]C[ #1,#2 ]2^(d-Length[ #1 ]-Length[ #2 ])&,P[ p ],P[ d-p ],1 ],{p,0,d} ]/(d!2^d) ];AC[ 5 ] (* End *)
Extensions
Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 11 2007
Comments