Information on Result #614399

Linear OA(724, 49, F7, 16) (dual of [49, 25, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16

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(724, 49, F7, 15) (dual of [49, 25, 16]-code) [i]Strength Reduction
2Linear OA(731, 68, F7, 16) (dual of [68, 37, 17]-code) [i]VarÅ¡amov–Edel Lengthening
3Linear OA(726, 53, F7, 16) (dual of [53, 27, 17]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
4Linear OA(728, 53, F7, 18) (dual of [53, 25, 19]-code) [i]✔
5Linear OA(727, 56, F7, 16) (dual of [56, 29, 17]-code) [i]✔
6Linear OA(729, 60, F7, 16) (dual of [60, 31, 17]-code) [i]✔
7Linear OA(727, 57, F7, 15) (dual of [57, 30, 16]-code) [i]✔
8Linear OA(726, 57, F7, 14) (dual of [57, 31, 15]-code) [i]✔
9Linear OA(735, 60, F7, 20) (dual of [60, 25, 21]-code) [i]✔
10Linear OA(731, 64, F7, 16) (dual of [64, 33, 17]-code) [i]✔
11Linear OA(742, 67, F7, 24) (dual of [67, 25, 25]-code) [i]✔
12Linear OA(744, 69, F7, 25) (dual of [69, 25, 26]-code) [i]✔
13Linear OA(749, 74, F7, 26) (dual of [74, 25, 27]-code) [i]✔
14Linear OA(730, 63, F7, 16) (dual of [63, 33, 17]-code) [i]✔
15Linear OA(739, 64, F7, 22) (dual of [64, 25, 23]-code) [i]✔
16Linear OA(745, 71, F7, 24) (dual of [71, 26, 25]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes
17Linear OA(738, 64, F7, 20) (dual of [64, 26, 21]-code) [i]✔
18Linear OA(734, 60, F7, 19) (dual of [60, 26, 20]-code) [i]✔
19Linear OA(728, 58, F7, 16) (dual of [58, 30, 17]-code) [i]✔
20Linear OA(729, 61, F7, 15) (dual of [61, 32, 16]-code) [i]✔
21Linear OA(740, 65, F7, 23) (dual of [65, 25, 24]-code) [i]✔
22Linear OA(731, 65, F7, 16) (dual of [65, 34, 17]-code) [i]✔