Information on Result #1613496
Linear OOA(8145, 3287, F81, 4, 21) (dual of [(3287, 4), 13103, 22]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(8145, 3287, F81, 2, 21) (dual of [(3287, 2), 6529, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8145, 6574, F81, 21) (dual of [6574, 6529, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(8145, 6575, F81, 21) (dual of [6575, 6530, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(15) [i] based on
- linear OA(8141, 6561, F81, 21) (dual of [6561, 6520, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(8131, 6561, F81, 16) (dual of [6561, 6530, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(814, 14, F81, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,81)), using
- discarding factors / shortening the dual code based on linear OA(814, 81, F81, 4) (dual of [81, 77, 5]-code or 81-arc in PG(3,81)), using
- Reed–Solomon code RS(77,81) [i]
- discarding factors / shortening the dual code based on linear OA(814, 81, F81, 4) (dual of [81, 77, 5]-code or 81-arc in PG(3,81)), using
- construction X applied to Ce(20) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(8145, 6575, F81, 21) (dual of [6575, 6530, 22]-code), using
Mode: 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(8145, 1095, F81, 28, 21) (dual of [(1095, 28), 30615, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |