Information on Result #613615

Linear OA(550, 78125, F5, 9) (dual of [78125, 78075, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(554, 78131, F5, 9) (dual of [78131, 78077, 10]-code) [i](u, u+v)-Construction
2Linear OA(555, 78136, F5, 9) (dual of [78136, 78081, 10]-code) [i]
3Linear OA(556, 78145, F5, 9) (dual of [78145, 78089, 10]-code) [i]
4Linear OOA(550, 66012, F5, 2, 9) (dual of [(66012, 2), 131974, 10]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
5Linear OOA(550, 66012, F5, 3, 9) (dual of [(66012, 3), 197986, 10]-NRT-code) [i]
6Digital (41, 50, 66012)-net over F5 [i]
7Linear OA(558, 78133, F5, 11) (dual of [78133, 78075, 12]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
8Linear OA(550, 78132, F5, 9) (dual of [78132, 78082, 10]-code) [i]✔
9Linear OA(567, 78142, F5, 12) (dual of [78142, 78075, 13]-code) [i]✔
10Linear OA(551, 78140, F5, 9) (dual of [78140, 78089, 10]-code) [i]✔
11Linear OA(575, 78150, F5, 13) (dual of [78150, 78075, 14]-code) [i]✔
12Linear OA(553, 78149, F5, 9) (dual of [78149, 78096, 10]-code) [i]✔
13Linear OA(586, 78161, F5, 14) (dual of [78161, 78075, 15]-code) [i]✔
14Linear OA(595, 78170, F5, 15) (dual of [78170, 78075, 16]-code) [i]✔
15Linear OA(584, 78155, F5, 14) (dual of [78155, 78071, 15]-code) [i]✔
16Linear OA(585, 78160, F5, 14) (dual of [78160, 78075, 15]-code) [i]✔
17Linear OA(556, 78155, F5, 9) (dual of [78155, 78099, 10]-code) [i]✔
18Linear OA(596, 78170, F5, 16) (dual of [78170, 78074, 17]-code) [i]✔
19Linear OA(594, 78169, F5, 15) (dual of [78169, 78075, 16]-code) [i]✔
20Linear OA(585, 78156, F5, 14) (dual of [78156, 78071, 15]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes
21Linear OA(584, 78154, F5, 14) (dual of [78154, 78070, 15]-code) [i]✔
22Linear OA(583, 78152, F5, 14) (dual of [78152, 78069, 15]-code) [i]✔
23Linear OA(578, 78155, F5, 13) (dual of [78155, 78077, 14]-code) [i]✔
24Linear OA(576, 78152, F5, 13) (dual of [78152, 78076, 14]-code) [i]✔
25Linear OA(566, 78135, F5, 12) (dual of [78135, 78069, 13]-code) [i]✔
26Linear OA(559, 78135, F5, 11) (dual of [78135, 78076, 12]-code) [i]✔
27Linear OA(556, 78154, F5, 9) (dual of [78154, 78098, 10]-code) [i]✔
28Linear OA(555, 78152, F5, 9) (dual of [78152, 78097, 10]-code) [i]✔
29Linear OA(551, 78141, F5, 9) (dual of [78141, 78090, 10]-code) [i]✔Construction X4 with Extended Narrow-Sense BCH Codes