Information on Result #732102
Linear OA(1655, 4186, F16, 15) (dual of [4186, 4131, 16]-code), using (u, u+v)-construction based on
- linear OA(1612, 87, F16, 7) (dual of [87, 75, 8]-code), using
- construction X applied to C([5,11]) ⊂ C([6,11]) [i] based on
- linear OA(1612, 85, F16, 7) (dual of [85, 73, 8]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {5,6,…,11}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(1610, 85, F16, 6) (dual of [85, 75, 7]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {6,7,…,11}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(160, 2, F16, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to C([5,11]) ⊂ C([6,11]) [i] based on
- linear OA(1643, 4099, F16, 15) (dual of [4099, 4056, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(13) [i] based on
- linear OA(1643, 4096, F16, 15) (dual of [4096, 4053, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(1640, 4096, F16, 14) (dual of [4096, 4056, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(160, 3, F16, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s (see above)
- construction X applied to Ce(14) ⊂ Ce(13) [i] based on
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 OOA(1655, 2093, F16, 2, 15) (dual of [(2093, 2), 4131, 16]-NRT-code) | [i] | OOA Folding | |