NonZeroWtC17PX;
save Code71714, D:\\coding new\\Coding Theory\\DataOutD7Xt\\CdD7k17r14.m;
Eksplorasi dilanjutkan:
read D:\\coding new\\Coding Theory\\DataOutD7Xt\\CdD7k17r14.m;
nopsCode71714;
B6:=Code71714[1];
i:=17: B5:=DelVekMi,B6:
i:=16: B4:=DelVekMi,B5:
i:=15: B3:=DelVekMi,B4:
i:=14: B2:=DelVekMi,B3:
i:=12: B1:=DelVekMi,B2:
i:=9: B:=DelVekMi,B1;
M:=UbahMtxCRB;
r:=M[2]; d:=7: k:=B[1];
t:=mind-1,k; L:=ListKombMM,t:
H:=Kolek1VekMd,r,r,L: nopsH;
P:=[{},{seqi,i=1..nopsH}]: K:=IdxAddXVd,P,H,L,0,6:
nopsK;
save K, D:\\coding new\\Coding Theory\\DataOutD7Xt\\DatKD7.m;
read D:\\coding new\\Coding Theory\\DataOutD7Xt\\DatKD7.m; H5:=DefHXK,H: nopsH5;
H6:=KolekXVMd,K,H,L: nopsH6;
Q:=ReduEkiXH5,M: nopsQ;
Akhirnya,
diperoleh 4 kode optimal [31,17,7] tidak saling ekivalen.
T:=mapX-AddVekMXX,M,Q: Code71714:=mapX-UbahMtxRCX,T:
C17PX:=Code71714[4];
NonZeroWtC17PX;
save Code71714, D:\\coding new\\Coding Theory\\DataOutD7Xt\\CdD7k17r14.m;
ABSTRACT
ASRIZA RAHMA. Construction of Strongly Optimal Linear Binary Codes with Minimum Distance of 5 and 7. Under supervision of SUGI GURITMAN and
NUR ALIATININGTYAS.
A code which is also a subspace of
is called linear binary code. If C has length n, dimension k and minimum distance d, then C is an [n, k, d]
code. The main problem in coding theory is optimizing one of the parameters n, k, and d for given values of the others. In this research, the strongly optimal linear
binary codes are constructed by using Gilbert-Varshamov bound and implemented using MAPLE software. In this case, the constructed basic code C[n, k, d] is then
extended to obtain the code
[ , , ], which can not be extended anymore and
which is known from the previus research that [ +1,
+1,d] does not exist. As a result,
[ , , ] is strongly optimal code. The strongly optimal codes that
has been successfully constructed are the codes with parameters [8,2,5], [11,4,5], [17,9,5], [23,14,5], [31,21,5], [33,23,5], [11,2,7], [15,5,7], [23,12,7], [27,14,7],
[30,16,7] and [31,17,7].
Keywords: linear binary codes, strongly optimal, and minimum distance.
