Information on Result #898473
Linear OOA(16107, 524355, F16, 2, 20) (dual of [(524355, 2), 1048603, 21]-NRT-code), using (u, u+v)-construction based on
- linear OOA(1616, 65, F16, 2, 10) (dual of [(65, 2), 114, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,119P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- extended algebraic-geometric NRT-code AGe(2;F,119P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- linear OOA(1691, 524290, F16, 2, 20) (dual of [(524290, 2), 1048489, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(1691, 1048580, F16, 20) (dual of [1048580, 1048489, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(1691, 1048581, F16, 20) (dual of [1048581, 1048490, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- linear OA(1691, 1048576, F16, 20) (dual of [1048576, 1048485, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(1686, 1048576, F16, 19) (dual of [1048576, 1048490, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(19) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(1691, 1048581, F16, 20) (dual of [1048581, 1048490, 21]-code), using
- OOA 2-folding [i] based on linear OA(1691, 1048580, F16, 20) (dual of [1048580, 1048489, 21]-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(16107, 104870, F16, 22, 20) (dual of [(104870, 22), 2307033, 21]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |