Information on Result #902132
Linear OOA(3278, 524367, F32, 2, 17) (dual of [(524367, 2), 1048656, 18]-NRT-code), using (u, u+v)-construction based on
- linear OOA(3213, 77, F32, 2, 8) (dual of [(77, 2), 141, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(324, 33, F32, 2, 4) (dual of [(33, 2), 62, 5]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;62,32) [i]
- 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(324, 33, F32, 2, 4) (dual of [(33, 2), 62, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(3265, 524290, F32, 2, 17) (dual of [(524290, 2), 1048515, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3265, 1048580, F32, 17) (dual of [1048580, 1048515, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(3265, 1048576, F32, 17) (dual of [1048576, 1048511, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(3261, 1048576, F32, 16) (dual of [1048576, 1048515, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(320, 4, F32, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- OOA 2-folding [i] based on linear OA(3265, 1048580, F32, 17) (dual of [1048580, 1048515, 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(3278, 131091, F32, 18, 17) (dual of [(131091, 18), 2359560, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |