Information on Result #614434

Linear OA(727, 49, F7, 18) (dual of [49, 22, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18

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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(729, 51, F7, 19) (dual of [51, 22, 20]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
2Linear OA(727, 51, F7, 18) (dual of [51, 24, 19]-code) [i]✔
3Linear OA(732, 54, F7, 20) (dual of [54, 22, 21]-code) [i]✔
4Linear OA(728, 53, F7, 18) (dual of [53, 25, 19]-code) [i]✔
5Linear OA(739, 60, F7, 24) (dual of [60, 21, 25]-code) [i]✔
6Linear OA(740, 62, F7, 24) (dual of [62, 22, 25]-code) [i]✔
7Linear OA(738, 60, F7, 23) (dual of [60, 22, 24]-code) [i]✔
8Linear OA(736, 57, F7, 22) (dual of [57, 21, 23]-code) [i]✔
9Linear OA(735, 57, F7, 21) (dual of [57, 22, 22]-code) [i]✔
10Linear OA(731, 57, F7, 18) (dual of [57, 26, 19]-code) [i]✔
11Linear OA(732, 59, F7, 18) (dual of [59, 27, 19]-code) [i]✔
12Linear OA(742, 64, F7, 25) (dual of [64, 22, 26]-code) [i]✔
13Linear OA(734, 63, F7, 18) (dual of [63, 29, 19]-code) [i]✔
14Linear OA(745, 67, F7, 26) (dual of [67, 22, 27]-code) [i]✔
15Linear OA(735, 66, F7, 18) (dual of [66, 31, 19]-code) [i]✔
16Linear OA(748, 69, F7, 27) (dual of [69, 21, 28]-code) [i]✔
17Linear OA(739, 61, F7, 24) (dual of [61, 22, 25]-code) [i]✔
18Linear OA(741, 63, F7, 25) (dual of [63, 22, 26]-code) [i]✔
19Linear OA(737, 58, F7, 23) (dual of [58, 21, 24]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes
20Linear OA(738, 61, F7, 22) (dual of [61, 23, 23]-code) [i]✔
21Linear OA(733, 61, F7, 18) (dual of [61, 28, 19]-code) [i]✔