Information on Result #735312
Linear OA(8172, 531544, F81, 21) (dual of [531544, 531472, 22]-code), using (u, u+v)-construction based on
- linear OA(8111, 100, F81, 10) (dual of [100, 89, 11]-code), using
- extended algebraic-geometric code AGe(F,89P) [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- linear OA(8161, 531444, F81, 21) (dual of [531444, 531383, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- 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(8158, 531441, F81, 20) (dual of [531441, 531383, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(20) ⊂ Ce(19) [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(2796, 531544, S27, 21) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(8172, 265772, F81, 2, 21) (dual of [(265772, 2), 531472, 22]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(8172, 177181, F81, 3, 21) (dual of [(177181, 3), 531471, 22]-NRT-code) | [i] | ||