Information on Result #735291
Linear OA(8175, 531526, F81, 22) (dual of [531526, 531451, 23]-code), using (u, u+v)-construction based on
- linear OA(8111, 82, F81, 11) (dual of [82, 71, 12]-code or 82-arc in PG(10,81)), using
- extended Reed–Solomon code RSe(71,81) [i]
- the expurgated narrow-sense BCH-code C(I) with length 82 | 812−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(8164, 531444, F81, 22) (dual of [531444, 531380, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(8164, 531441, F81, 22) (dual of [531441, 531377, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(8161, 531441, F81, 21) (dual of [531441, 531380, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(810, 3, F81, 0) (dual of [3, 3, 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(21) ⊂ Ce(20) [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 | OA(27100, 531526, S27, 22) | [i] | Discarding Parts of the Base for OAs | |
2 | Linear OOA(8175, 265763, F81, 2, 22) (dual of [(265763, 2), 531451, 23]-NRT-code) | [i] | OOA Folding | |
3 | Linear OOA(8175, 177175, F81, 3, 22) (dual of [(177175, 3), 531450, 23]-NRT-code) | [i] |