Information on Result #734339
Linear OA(3252, 32820, F32, 15) (dual of [32820, 32768, 16]-code), using (u, u+v)-construction based on
- linear OA(328, 44, F32, 7) (dual of [44, 36, 8]-code), using
- extended algebraic-geometric code AGe(F,36P) [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- linear OA(3244, 32776, F32, 15) (dual of [32776, 32732, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([0,6]) [i] based on
- linear OA(3243, 32769, F32, 15) (dual of [32769, 32726, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(3237, 32769, F32, 13) (dual of [32769, 32732, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (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, using
- construction X applied to C([0,7]) ⊂ C([0,6]) [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(3252, 16410, F32, 2, 15) (dual of [(16410, 2), 32768, 16]-NRT-code) | [i] | OOA Folding | |