Information on Result #721513
Linear OA(1611, 259, F16, 6) (dual of [259, 248, 7]-code), using construction XX applied to C1 = C([254,3]), C2 = C([0,4]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C([254,4]) based on
- linear OA(169, 255, F16, 5) (dual of [255, 246, 6]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−1,0,1,2,3}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(169, 255, F16, 5) (dual of [255, 246, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(1611, 255, F16, 6) (dual of [255, 244, 7]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−1,0,…,4}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(167, 255, F16, 4) (dual of [255, 248, 5]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [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 | OA(815, 259, S8, 6) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OA(1672, 1048840, F16, 13) (dual of [1048840, 1048768, 14]-code) | [i] | (u, u+v)-Construction | |