Information on Result #898394
Linear OOA(1689, 524352, F16, 2, 16) (dual of [(524352, 2), 1048615, 17]-NRT-code), using (u, u+v)-construction based on
- linear OOA(1614, 65, F16, 2, 8) (dual of [(65, 2), 116, 9]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,121P) [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,121P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- linear OOA(1675, 524287, F16, 2, 16) (dual of [(524287, 2), 1048499, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(1675, 1048574, F16, 16) (dual of [1048574, 1048499, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(1675, 1048575, F16, 16) (dual of [1048575, 1048500, 17]-code), using
- 1 times truncation [i] based on linear OA(1676, 1048576, F16, 17) (dual of [1048576, 1048500, 18]-code), using
- an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- 1 times truncation [i] based on linear OA(1676, 1048576, F16, 17) (dual of [1048576, 1048500, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(1675, 1048575, F16, 16) (dual of [1048575, 1048500, 17]-code), using
- OOA 2-folding [i] based on linear OA(1675, 1048574, F16, 16) (dual of [1048574, 1048499, 17]-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(1689, 131087, F16, 18, 16) (dual of [(131087, 18), 2359477, 17]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |