Information on Result #735210
Linear OA(8166, 6645, F81, 27) (dual of [6645, 6579, 28]-code), using (u, u+v)-construction based on
- linear OA(8113, 82, F81, 13) (dual of [82, 69, 14]-code or 82-arc in PG(12,81)), using
- extended Reed–Solomon code RSe(69,81) [i]
- the expurgated narrow-sense BCH-code C(I) with length 82 | 812−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(8153, 6563, F81, 27) (dual of [6563, 6510, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- 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(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(810, 2, F81, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
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(8166, 2215, F81, 3, 27) (dual of [(2215, 3), 6579, 28]-NRT-code) | [i] | OOA Folding | |