Information on Result #902134
Linear OOA(3275, 524337, F32, 2, 17) (dual of [(524337, 2), 1048599, 18]-NRT-code), using (u, u+v)-construction based on
- linear OOA(329, 44, F32, 2, 8) (dual of [(44, 2), 79, 9]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,79P) [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- linear OOA(3266, 524293, F32, 2, 17) (dual of [(524293, 2), 1048520, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3266, 1048586, F32, 17) (dual of [1048586, 1048520, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,7]) [i] based on
- linear OA(3265, 1048577, F32, 17) (dual of [1048577, 1048512, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(3257, 1048577, F32, 15) (dual of [1048577, 1048520, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(321, 9, F32, 1) (dual of [9, 8, 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([0,8]) ⊂ C([0,7]) [i] based on
- OOA 2-folding [i] based on linear OA(3266, 1048586, F32, 17) (dual of [1048586, 1048520, 18]-code), using
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(3275, 131084, F32, 18, 17) (dual of [(131084, 18), 2359437, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |