Information on Result #696693
Linear OA(3291, 1048622, F32, 21) (dual of [1048622, 1048531, 22]-code), using construction X applied to Ce(20) ⊂ Ce(11) based on
- linear OA(3281, 1048576, F32, 21) (dual of [1048576, 1048495, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(3245, 1048576, F32, 12) (dual of [1048576, 1048531, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(3210, 46, F32, 8) (dual of [46, 36, 9]-code), using
- construction X applied to AG(F,34P) ⊂ AG(F,36P) [i] based on
- linear OA(329, 43, F32, 8) (dual of [43, 34, 9]-code), using algebraic-geometric code AG(F,34P) [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- linear OA(327, 43, F32, 6) (dual of [43, 36, 7]-code), using algebraic-geometric code AG(F,36P) [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44 (see above)
- linear OA(321, 3, F32, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, s, F32, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to AG(F,34P) ⊂ AG(F,36P) [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(3291, 524311, F32, 2, 21) (dual of [(524311, 2), 1048531, 22]-NRT-code) | [i] | OOA Folding | |