Information on Result #691799
Linear OA(1678, 65545, F16, 21) (dual of [65545, 65467, 22]-code), using construction X applied to Ce(20) ⊂ Ce(18) based on
- linear OA(1677, 65536, F16, 21) (dual of [65536, 65459, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(1669, 65536, F16, 19) (dual of [65536, 65467, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(161, 9, F16, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-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 | OA(8104, 65545, S8, 21) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(1678, 40075, F16, 2, 21) (dual of [(40075, 2), 80072, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (57, 78, 40075)-net over F16 | [i] | ||
| 4 | Linear OOA(1678, 32772, F16, 2, 21) (dual of [(32772, 2), 65466, 22]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(1678, 6554, F16, 21, 21) (dual of [(6554, 21), 137556, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |