Information on Result #898258
Linear OOA(1646, 524314, F16, 2, 9) (dual of [(524314, 2), 1048582, 10]-NRT-code), using (u, u+v)-construction based on
- linear OOA(165, 24, F16, 2, 4) (dual of [(24, 2), 43, 5]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,43P) [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 24, using
- linear OOA(1641, 524290, F16, 2, 9) (dual of [(524290, 2), 1048539, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(1641, 1048580, F16, 9) (dual of [1048580, 1048539, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(1641, 1048581, F16, 9) (dual of [1048581, 1048540, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- linear OA(1641, 1048576, F16, 9) (dual of [1048576, 1048535, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(1636, 1048576, F16, 8) (dual of [1048576, 1048540, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(160, 5, F16, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(1641, 1048581, F16, 9) (dual of [1048581, 1048540, 10]-code), using
- OOA 2-folding [i] based on linear OA(1641, 1048580, F16, 9) (dual of [1048580, 1048539, 10]-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(1646, 262156, F16, 10, 9) (dual of [(262156, 10), 2621514, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |