Information on Result #733956
Linear OA(32101, 32876, F32, 27) (dual of [32876, 32775, 28]-code), using (u, u+v)-construction based on
- linear OA(3221, 100, F32, 13) (dual of [100, 79, 14]-code), using
- construction X applied to AG(F,83P) ⊂ AG(F,85P) [i] based on
- linear OA(3220, 97, F32, 13) (dual of [97, 77, 14]-code), using algebraic-geometric code AG(F,83P) [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- linear OA(3218, 97, F32, 11) (dual of [97, 79, 12]-code), using algebraic-geometric code AG(F,85P) [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98 (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,83P) ⊂ AG(F,85P) [i] based on
- linear OA(3280, 32776, F32, 27) (dual of [32776, 32696, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,12]) [i] based on
- linear OA(3279, 32769, F32, 27) (dual of [32769, 32690, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(3273, 32769, F32, 25) (dual of [32769, 32696, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(321, 7, F32, 1) (dual of [7, 6, 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 (see above)
- construction X applied to C([0,13]) ⊂ C([0,12]) [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(32101, 16438, F32, 2, 27) (dual of [(16438, 2), 32775, 28]-NRT-code) | [i] | OOA Folding | |