Information on Result #731567
Linear OA(1650, 131076, F16, 13) (dual of [131076, 131026, 14]-code), using trace code based on linear OA(25625, 65538, F256, 13) (dual of [65538, 65513, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- linear OA(25625, 65536, F256, 13) (dual of [65536, 65511, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(25623, 65536, F256, 12) (dual of [65536, 65513, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
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:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(1651, 131077, F16, 13) (dual of [131077, 131026, 14]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(1657, 131100, F16, 13) (dual of [131100, 131043, 14]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(1658, 131109, F16, 13) (dual of [131109, 131051, 14]-code) | [i] | ||
| 4 | Linear OA(1659, 131114, F16, 13) (dual of [131114, 131055, 14]-code) | [i] | ||
| 5 | Linear OA(1660, 131161, F16, 13) (dual of [131161, 131101, 14]-code) | [i] | ||
| 6 | Linear OOA(1650, 65538, F16, 2, 13) (dual of [(65538, 2), 131026, 14]-NRT-code) | [i] | OOA Folding | |