Information on Result #700458
Linear OA(25649, 65562, F256, 21) (dual of [65562, 65513, 22]-code), using construction X applied to Ce(20) ⊂ Ce(11) based on
- linear OA(25641, 65536, F256, 21) (dual of [65536, 65495, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(25623, 65536, F256, 12) (dual of [65536, 65513, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(2568, 26, F256, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,256)), using
- discarding factors / shortening the dual code based on linear OA(2568, 256, F256, 8) (dual of [256, 248, 9]-code or 256-arc in PG(7,256)), using
- Reed–Solomon code RS(248,256) [i]
- discarding factors / shortening the dual code based on linear OA(2568, 256, F256, 8) (dual of [256, 248, 9]-code or 256-arc in PG(7,256)), 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(12856, 65562, S128, 21) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(25649, 37718, F256, 2, 21) (dual of [(37718, 2), 75387, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(25649, 37718, F256, 3, 21) (dual of [(37718, 3), 113105, 22]-NRT-code) | [i] | ||
| 4 | Linear OOA(25649, 37718, F256, 4, 21) (dual of [(37718, 4), 150823, 22]-NRT-code) | [i] | ||
| 5 | Linear OOA(25649, 37718, F256, 5, 21) (dual of [(37718, 5), 188541, 22]-NRT-code) | [i] | ||
| 6 | Linear OOA(25649, 37718, F256, 6, 21) (dual of [(37718, 6), 226259, 22]-NRT-code) | [i] | ||
| 7 | Digital (28, 49, 37718)-net over F256 | [i] | ||
| 8 | Linear OOA(25649, 32781, F256, 2, 21) (dual of [(32781, 2), 65513, 22]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(25649, 21854, F256, 3, 21) (dual of [(21854, 3), 65513, 22]-NRT-code) | [i] | ||
| 10 | Linear OOA(25649, 10927, F256, 6, 21) (dual of [(10927, 6), 65513, 22]-NRT-code) | [i] | ||
| 11 | Linear OOA(25649, 6556, F256, 21, 21) (dual of [(6556, 21), 137627, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |