Information on Result #721319
Linear OA(1622, 90, F16, 12) (dual of [90, 68, 13]-code), using construction XX applied to C1 = C([12,22]), C2 = C([11,20]), C3 = C1 + C2 = C([12,20]), and C∩ = C1 ∩ C2 = C([11,22]) based on
- linear OA(1619, 85, F16, 11) (dual of [85, 66, 12]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {12,13,…,22}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(1619, 85, F16, 10) (dual of [85, 66, 11]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {11,12,…,20}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(1621, 85, F16, 12) (dual of [85, 64, 13]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {11,12,…,22}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(1617, 85, F16, 9) (dual of [85, 68, 10]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {12,13,…,20}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(161, 3, F16, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, 16, F16, 1) (dual of [16, 15, 2]-code), using
- Reed–Solomon code RS(15,16) [i]
- discarding factors / shortening the dual code based on linear OA(161, 16, F16, 1) (dual of [16, 15, 2]-code), using
- 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
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(1622, 45, F16, 2, 12) (dual of [(45, 2), 68, 13]-NRT-code) | [i] | OOA Folding | |