Information on Result #611910

Linear OA(3127, 19683, F3, 22) (dual of [19683, 19556, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22

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(3126, 19682, F3, 21) (dual of [19682, 19556, 22]-code) [i]Truncation
2Linear OA(3138, 19695, F3, 22) (dual of [19695, 19557, 23]-code) [i](u, u+v)-Construction
3Linear OA(3136, 19692, F3, 23) (dual of [19692, 19556, 24]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
4Linear OA(3128, 19693, F3, 22) (dual of [19693, 19565, 23]-code) [i]✔
5Linear OA(3146, 19702, F3, 24) (dual of [19702, 19556, 25]-code) [i]✔
6Linear OA(3148, 19696, F3, 25) (dual of [19696, 19548, 26]-code) [i]✔
7Linear OA(3149, 19705, F3, 25) (dual of [19705, 19556, 26]-code) [i]✔
8Linear OA(3130, 19696, F3, 22) (dual of [19696, 19566, 23]-code) [i]✔
9Linear OA(3131, 19705, F3, 22) (dual of [19705, 19574, 23]-code) [i]✔
10Linear OA(3160, 19716, F3, 26) (dual of [19716, 19556, 27]-code) [i]✔
11Linear OA(3134, 19710, F3, 22) (dual of [19710, 19576, 23]-code) [i]✔
12Linear OA(3135, 19718, F3, 22) (dual of [19718, 19583, 23]-code) [i]✔
13Linear OA(3133, 19716, F3, 21) (dual of [19716, 19583, 22]-code) [i]✔
14Linear OA(3174, 19724, F3, 28) (dual of [19724, 19550, 29]-code) [i]✔
15Linear OA(3175, 19731, F3, 28) (dual of [19731, 19556, 29]-code) [i]✔
16Linear OA(3171, 19724, F3, 27) (dual of [19724, 19553, 28]-code) [i]✔
17Linear OA(3172, 19728, F3, 27) (dual of [19728, 19556, 28]-code) [i]✔
18Linear OA(3138, 19724, F3, 22) (dual of [19724, 19586, 23]-code) [i]✔
19Linear OA(3139, 19731, F3, 22) (dual of [19731, 19592, 23]-code) [i]✔
20Linear OA(3135, 19724, F3, 21) (dual of [19724, 19589, 22]-code) [i]✔
21Linear OA(3136, 19728, F3, 21) (dual of [19728, 19592, 22]-code) [i]✔
22Linear OA(3188, 19744, F3, 29) (dual of [19744, 19556, 30]-code) [i]✔
23Linear OA(3198, 19754, F3, 30) (dual of [19754, 19556, 31]-code) [i]✔
24Linear OA(3173, 19722, F3, 28) (dual of [19722, 19549, 29]-code) [i]✔
25Linear OA(3174, 19730, F3, 28) (dual of [19730, 19556, 29]-code) [i]✔
26Linear OA(3137, 19722, F3, 22) (dual of [19722, 19585, 23]-code) [i]✔
27Linear OA(3138, 19730, F3, 22) (dual of [19730, 19592, 23]-code) [i]✔
28Linear OA(3186, 19736, F3, 29) (dual of [19736, 19550, 30]-code) [i]✔
29Linear OA(3187, 19743, F3, 29) (dual of [19743, 19556, 30]-code) [i]✔
30Linear OA(3197, 19753, F3, 30) (dual of [19753, 19556, 31]-code) [i]✔
31Linear OA(3148, 19697, F3, 25) (dual of [19697, 19549, 26]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes
32Linear OA(3150, 19709, F3, 24) (dual of [19709, 19559, 25]-code) [i]✔
33Linear OA(3149, 19707, F3, 24) (dual of [19707, 19558, 25]-code) [i]✔
34Linear OA(3139, 19697, F3, 23) (dual of [19697, 19558, 24]-code) [i]✔
35Linear OA(3130, 19697, F3, 22) (dual of [19697, 19567, 23]-code) [i]✔
36Linear OA(3132, 19709, F3, 21) (dual of [19709, 19577, 22]-code) [i]✔
37Linear OA(3131, 19707, F3, 21) (dual of [19707, 19576, 22]-code) [i]✔
38Linear OOA(3127, 9841, F3, 2, 22) (dual of [(9841, 2), 19555, 23]-NRT-code) [i]OOA Folding
39Linear OOA(3127, 6561, F3, 3, 22) (dual of [(6561, 3), 19556, 23]-NRT-code) [i]
40Linear OOA(3127, 4920, F3, 4, 22) (dual of [(4920, 4), 19553, 23]-NRT-code) [i]
41Linear OOA(3127, 3936, F3, 5, 22) (dual of [(3936, 5), 19553, 23]-NRT-code) [i]
42Linear OOA(3127, 1789, F3, 22, 22) (dual of [(1789, 22), 39231, 23]-NRT-code) [i]OA Folding and Stacking