Information on Result #617566

Linear OA(2758, 19683, F27, 20) (dual of [19683, 19625, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20

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(2768, 19711, F27, 20) (dual of [19711, 19643, 21]-code) [i](u, u+v)-Construction
2Linear OA(2769, 19721, F27, 20) (dual of [19721, 19652, 21]-code) [i]
3Linear OA(2770, 19731, F27, 20) (dual of [19731, 19661, 21]-code) [i]
4Linear OA(2771, 19735, F27, 20) (dual of [19735, 19664, 21]-code) [i]
5Linear OA(2772, 19747, F27, 20) (dual of [19747, 19675, 21]-code) [i]
6Linear OA(2773, 19751, F27, 20) (dual of [19751, 19678, 21]-code) [i]
7Linear OA(2774, 19759, F27, 20) (dual of [19759, 19685, 21]-code) [i]
8Linear OA(2775, 19788, F27, 20) (dual of [19788, 19713, 21]-code) [i]
9Linear OA(2776, 19866, F27, 20) (dual of [19866, 19790, 21]-code) [i]
10Linear OA(2775, 19701, F27, 20) (dual of [19701, 19626, 21]-code) [i]Generalized (u, u+v)-Construction
11Linear OA(2776, 19704, F27, 20) (dual of [19704, 19628, 21]-code) [i]
12Linear OOA(2758, 9895, F27, 2, 20) (dual of [(9895, 2), 19732, 21]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
13Digital (38, 58, 9895)-net over F27 [i]
14Linear OA(2771, 19697, F27, 20) (dual of [19697, 19626, 21]-code) [i](u, u−v, u+v+w)-Construction
15Linear OA(2772, 19699, F27, 20) (dual of [19699, 19627, 21]-code) [i]
16Linear OA(2773, 19701, F27, 20) (dual of [19701, 19628, 21]-code) [i]
17Linear OA(2774, 19739, F27, 20) (dual of [19739, 19665, 21]-code) [i]
18Linear OA(2775, 19749, F27, 20) (dual of [19749, 19674, 21]-code) [i]
19Linear OA(2776, 19759, F27, 20) (dual of [19759, 19683, 21]-code) [i]
20Linear OA(2761, 19686, F27, 21) (dual of [19686, 19625, 22]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
21Linear OA(2758, 19686, F27, 20) (dual of [19686, 19628, 21]-code) [i]✔
22Linear OA(2765, 19690, F27, 22) (dual of [19690, 19625, 23]-code) [i]✔
23Linear OA(2759, 19690, F27, 20) (dual of [19690, 19631, 21]-code) [i]✔
24Linear OA(2769, 19694, F27, 23) (dual of [19694, 19625, 24]-code) [i]✔
25Linear OA(2760, 19694, F27, 20) (dual of [19694, 19634, 21]-code) [i]✔
26Linear OA(2773, 19698, F27, 24) (dual of [19698, 19625, 25]-code) [i]✔
27Linear OA(2761, 19698, F27, 20) (dual of [19698, 19637, 21]-code) [i]✔
28Linear OA(2777, 19702, F27, 25) (dual of [19702, 19625, 26]-code) [i]✔
29Linear OA(2762, 19702, F27, 20) (dual of [19702, 19640, 21]-code) [i]✔
30Linear OA(2781, 19706, F27, 26) (dual of [19706, 19625, 27]-code) [i]✔
31Linear OA(2763, 19706, F27, 20) (dual of [19706, 19643, 21]-code) [i]✔
32Linear OA(2786, 19711, F27, 28) (dual of [19711, 19625, 29]-code) [i]✔
33Linear OA(2764, 19710, F27, 20) (dual of [19710, 19646, 21]-code) [i]✔
34Linear OA(2791, 19716, F27, 29) (dual of [19716, 19625, 30]-code) [i]✔
35Linear OA(2766, 19715, F27, 20) (dual of [19715, 19649, 21]-code) [i]✔
36Linear OA(2795, 19720, F27, 30) (dual of [19720, 19625, 31]-code) [i]✔
37Linear OA(2767, 19719, F27, 20) (dual of [19719, 19652, 21]-code) [i]✔
38Linear OA(27100, 19725, F27, 31) (dual of [19725, 19625, 32]-code) [i]✔
39Linear OA(2768, 19721, F27, 20) (dual of [19721, 19653, 21]-code) [i]✔
40Linear OA(2769, 19724, F27, 20) (dual of [19724, 19655, 21]-code) [i]✔
41Linear OA(27104, 19729, F27, 32) (dual of [19729, 19625, 33]-code) [i]✔
42Linear OA(27108, 19731, F27, 33) (dual of [19731, 19623, 34]-code) [i]✔
43Linear OA(27109, 19734, F27, 33) (dual of [19734, 19625, 34]-code) [i]✔
44Linear OA(2765, 19712, F27, 20) (dual of [19712, 19647, 21]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes
45Linear OOA(2758, 1968, F27, 20, 20) (dual of [(1968, 20), 39302, 21]-NRT-code) [i]OA Folding and Stacking