Information on Result #1613986
Linear OOA(8171, 3290, F81, 4, 33) (dual of [(3290, 4), 13089, 34]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(8171, 3290, F81, 2, 33) (dual of [(3290, 2), 6509, 34]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8171, 6580, F81, 33) (dual of [6580, 6509, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(8171, 6581, F81, 33) (dual of [6581, 6510, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(25) [i] based on
- linear OA(8165, 6561, F81, 33) (dual of [6561, 6496, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(8151, 6561, F81, 26) (dual of [6561, 6510, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(816, 20, F81, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,81)), using
- discarding factors / shortening the dual code based on linear OA(816, 81, F81, 6) (dual of [81, 75, 7]-code or 81-arc in PG(5,81)), using
- Reed–Solomon code RS(75,81) [i]
- discarding factors / shortening the dual code based on linear OA(816, 81, F81, 6) (dual of [81, 75, 7]-code or 81-arc in PG(5,81)), using
- construction X applied to Ce(32) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(8171, 6581, F81, 33) (dual of [6581, 6510, 34]-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(8171, 822, F81, 36, 33) (dual of [(822, 36), 29521, 34]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |