Information on Result #699579
Linear OA(8179, 6587, F81, 36) (dual of [6587, 6508, 37]-code), using construction X applied to Ce(35) ⊂ Ce(26) based on
- linear OA(8171, 6561, F81, 36) (dual of [6561, 6490, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(8153, 6561, F81, 27) (dual of [6561, 6508, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(818, 26, F81, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,81)), using
- discarding factors / shortening the dual code based on linear OA(818, 81, F81, 8) (dual of [81, 73, 9]-code or 81-arc in PG(7,81)), using
- Reed–Solomon code RS(73,81) [i]
- discarding factors / shortening the dual code based on linear OA(818, 81, F81, 8) (dual of [81, 73, 9]-code or 81-arc in PG(7,81)), 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(8179, 4027, F81, 2, 36) (dual of [(4027, 2), 7975, 37]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8179, 4027, F81, 3, 36) (dual of [(4027, 3), 12002, 37]-NRT-code) | [i] | ||
| 3 | Linear OOA(8179, 4027, F81, 4, 36) (dual of [(4027, 4), 16029, 37]-NRT-code) | [i] | ||
| 4 | Digital (43, 79, 4027)-net over F81 | [i] | ||
| 5 | Linear OOA(8179, 3293, F81, 2, 36) (dual of [(3293, 2), 6507, 37]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8179, 2195, F81, 3, 36) (dual of [(2195, 3), 6506, 37]-NRT-code) | [i] | ||