Information on Result #612053

Linear OA(3109, 729, F3, 28) (dual of [729, 620, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28

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(3123, 744, F3, 28) (dual of [744, 621, 29]-code) [i](u, u+v)-Construction
2Linear OA(3120, 776, F3, 28) (dual of [776, 656, 29]-code) [i]VarÅ¡amov–Edel Lengthening
3Linear OA(3121, 793, F3, 28) (dual of [793, 672, 29]-code) [i]
4Linear OA(3122, 814, F3, 28) (dual of [814, 692, 29]-code) [i]
5Linear OA(3123, 839, F3, 28) (dual of [839, 716, 29]-code) [i]
6Linear OA(3124, 868, F3, 28) (dual of [868, 744, 29]-code) [i]
7Linear OA(3125, 900, F3, 28) (dual of [900, 775, 29]-code) [i]
8Linear OA(3112, 732, F3, 29) (dual of [732, 620, 30]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
9Linear OA(3110, 736, F3, 28) (dual of [736, 626, 29]-code) [i]✔
10Linear OA(3119, 739, F3, 30) (dual of [739, 620, 31]-code) [i]✔
11Linear OA(3121, 741, F3, 31) (dual of [741, 620, 32]-code) [i]✔
12Linear OA(3112, 742, F3, 28) (dual of [742, 630, 29]-code) [i]✔
13Linear OA(3113, 745, F3, 28) (dual of [745, 632, 29]-code) [i]✔
14Linear OA(3129, 749, F3, 32) (dual of [749, 620, 33]-code) [i]✔
15Linear OA(3116, 754, F3, 28) (dual of [754, 638, 29]-code) [i]✔
16Linear OA(3114, 749, F3, 27) (dual of [749, 635, 28]-code) [i]✔
17Linear OA(3138, 757, F3, 34) (dual of [757, 619, 35]-code) [i]✔
18Linear OA(3140, 760, F3, 34) (dual of [760, 620, 35]-code) [i]✔
19Linear OA(3138, 758, F3, 33) (dual of [758, 620, 34]-code) [i]✔
20Linear OA(3117, 757, F3, 28) (dual of [757, 640, 29]-code) [i]✔
21Linear OA(3119, 763, F3, 28) (dual of [763, 644, 29]-code) [i]✔
22Linear OA(3117, 761, F3, 27) (dual of [761, 644, 28]-code) [i]✔
23Linear OA(3150, 769, F3, 35) (dual of [769, 619, 36]-code) [i]✔
24Linear OA(3151, 771, F3, 35) (dual of [771, 620, 36]-code) [i]✔
25Linear OA(3124, 770, F3, 28) (dual of [770, 646, 29]-code) [i]✔
26Linear OA(3125, 772, F3, 28) (dual of [772, 647, 29]-code) [i]✔
27Linear OA(3163, 783, F3, 37) (dual of [783, 620, 38]-code) [i]✔
28Linear OA(3159, 779, F3, 36) (dual of [779, 620, 37]-code) [i]✔
29Linear OA(3172, 792, F3, 38) (dual of [792, 620, 39]-code) [i]✔
30Linear OA(3181, 801, F3, 40) (dual of [801, 620, 41]-code) [i]✔
31Linear OA(3179, 799, F3, 39) (dual of [799, 620, 40]-code) [i]✔
32Linear OA(3143, 767, F3, 33) (dual of [767, 624, 34]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes
33Linear OA(3144, 767, F3, 34) (dual of [767, 623, 35]-code) [i]✔
34Linear OA(3142, 765, F3, 33) (dual of [765, 623, 34]-code) [i]✔
35Linear OA(3143, 765, F3, 34) (dual of [765, 622, 35]-code) [i]✔
36Linear OA(3141, 763, F3, 33) (dual of [763, 622, 34]-code) [i]✔
37Linear OA(3142, 763, F3, 34) (dual of [763, 621, 35]-code) [i]✔
38Linear OA(3140, 761, F3, 33) (dual of [761, 621, 34]-code) [i]✔
39Linear OA(3120, 738, F3, 31) (dual of [738, 618, 32]-code) [i]✔
40Linear OA(3122, 744, F3, 30) (dual of [744, 622, 31]-code) [i]✔
41Linear OA(3123, 744, F3, 31) (dual of [744, 621, 32]-code) [i]✔
42Linear OA(3121, 742, F3, 30) (dual of [742, 621, 31]-code) [i]✔
43Linear OA(3114, 735, F3, 29) (dual of [735, 621, 30]-code) [i]✔
44Linear OA(3111, 738, F3, 28) (dual of [738, 627, 29]-code) [i]✔
45Linear OA(3113, 747, F3, 27) (dual of [747, 634, 28]-code) [i]✔
46Linear OA(3115, 748, F3, 28) (dual of [748, 633, 29]-code) [i]✔
47Linear OOA(3109, 243, F3, 3, 28) (dual of [(243, 3), 620, 29]-NRT-code) [i]OOA Folding