Information on Result #721787
Linear OA(1671, 259, F16, 40) (dual of [259, 188, 41]-code), using construction XX applied to C1 = C([254,37]), C2 = C([0,38]), C3 = C1 + C2 = C([0,37]), and C∩ = C1 ∩ C2 = C([254,38]) based on
- linear OA(1669, 255, F16, 39) (dual of [255, 186, 40]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−1,0,…,37}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(1669, 255, F16, 39) (dual of [255, 186, 40]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,38], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(1671, 255, F16, 40) (dual of [255, 184, 41]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−1,0,…,38}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(1667, 255, F16, 38) (dual of [255, 188, 39]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,37], and designed minimum distance d ≥ |I|+1 = 39 [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
- linear OA(160, 2, F16, 0) (dual of [2, 2, 1]-code) (see above)
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(1677, 275, F16, 40) (dual of [275, 198, 41]-code) | [i] | Varšamov–Edel Lengthening | |
| 2 | Linear OA(1678, 287, F16, 40) (dual of [287, 209, 41]-code) | [i] | ||
| 3 | Linear OA(1679, 303, F16, 40) (dual of [303, 224, 41]-code) | [i] | ||