Information on Result #613772

Linear OA(5106, 78125, F5, 19) (dual of [78125, 78019, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19

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(5115, 78135, F5, 19) (dual of [78135, 78020, 20]-code) [i](u, u+v)-Construction
2Linear OA(5116, 78137, F5, 19) (dual of [78137, 78021, 20]-code) [i]
3Linear OA(5117, 78139, F5, 19) (dual of [78139, 78022, 20]-code) [i]
4Linear OA(5118, 78141, F5, 19) (dual of [78141, 78023, 20]-code) [i]
5Linear OA(5119, 78153, F5, 19) (dual of [78153, 78034, 20]-code) [i]
6Linear OA(5120, 78140, F5, 19) (dual of [78140, 78020, 20]-code) [i]Generalized (u, u+v)-Construction
7Linear OA(5119, 78139, F5, 19) (dual of [78139, 78020, 20]-code) [i](u, u−v, u+v+w)-Construction
8Linear OA(5114, 78133, F5, 21) (dual of [78133, 78019, 22]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
9Linear OA(5106, 78132, F5, 19) (dual of [78132, 78026, 20]-code) [i]✔
10Linear OA(5123, 78142, F5, 22) (dual of [78142, 78019, 23]-code) [i]✔
11Linear OA(5107, 78140, F5, 19) (dual of [78140, 78033, 20]-code) [i]✔
12Linear OA(5131, 78150, F5, 23) (dual of [78150, 78019, 24]-code) [i]✔
13Linear OA(5109, 78149, F5, 19) (dual of [78149, 78040, 20]-code) [i]✔
14Linear OA(5142, 78161, F5, 24) (dual of [78161, 78019, 25]-code) [i]✔
15Linear OA(5114, 78161, F5, 19) (dual of [78161, 78047, 20]-code) [i]✔
16Linear OA(5116, 78170, F5, 19) (dual of [78170, 78054, 20]-code) [i]✔
17Linear OA(5118, 78179, F5, 19) (dual of [78179, 78061, 20]-code) [i]✔
18Linear OA(5140, 78155, F5, 24) (dual of [78155, 78015, 25]-code) [i]✔
19Linear OA(5141, 78160, F5, 24) (dual of [78160, 78019, 25]-code) [i]✔
20Linear OA(5112, 78155, F5, 19) (dual of [78155, 78043, 20]-code) [i]✔
21Linear OA(5113, 78160, F5, 19) (dual of [78160, 78047, 20]-code) [i]✔
22Linear OA(5150, 78169, F5, 25) (dual of [78169, 78019, 26]-code) [i]✔
23Linear OA(5115, 78169, F5, 19) (dual of [78169, 78054, 20]-code) [i]✔
24Linear OA(5141, 78156, F5, 24) (dual of [78156, 78015, 25]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes
25Linear OA(5140, 78154, F5, 24) (dual of [78154, 78014, 25]-code) [i]✔
26Linear OA(5139, 78152, F5, 24) (dual of [78152, 78013, 25]-code) [i]✔
27Linear OA(5134, 78155, F5, 23) (dual of [78155, 78021, 24]-code) [i]✔
28Linear OA(5132, 78152, F5, 23) (dual of [78152, 78020, 24]-code) [i]✔
29Linear OA(5122, 78135, F5, 22) (dual of [78135, 78013, 23]-code) [i]✔
30Linear OA(5115, 78135, F5, 21) (dual of [78135, 78020, 22]-code) [i]✔
31Linear OA(5108, 78142, F5, 19) (dual of [78142, 78034, 20]-code) [i]✔
32Linear OA(5113, 78156, F5, 19) (dual of [78156, 78043, 20]-code) [i]✔
33Linear OA(5112, 78154, F5, 19) (dual of [78154, 78042, 20]-code) [i]✔
34Linear OA(5111, 78152, F5, 19) (dual of [78152, 78041, 20]-code) [i]✔
35Linear OA(5107, 78148, F5, 18) (dual of [78148, 78041, 19]-code) [i]✔Construction X4 with Extended Narrow-Sense BCH Codes