Information on Result #731989
Linear OA(16115, 4169, F16, 33) (dual of [4169, 4054, 34]-code), using (u, u+v)-construction based on
- linear OA(1622, 65, F16, 16) (dual of [65, 43, 17]-code), using
- extended algebraic-geometric code AGe(F,48P) [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 code AGe(F,48P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- linear OA(1693, 4104, F16, 33) (dual of [4104, 4011, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(29) [i] based on
- linear OA(1691, 4096, F16, 33) (dual of [4096, 4005, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(1685, 4096, F16, 30) (dual of [4096, 4011, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(162, 8, F16, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,16)), using
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- Reed–Solomon code RS(14,16) [i]
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- construction X applied to Ce(32) ⊂ Ce(29) [i] based on
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 OA(16114, 4168, F16, 32) (dual of [4168, 4054, 33]-code) | [i] | Truncation | |
| 2 | Linear OOA(16115, 2084, F16, 2, 33) (dual of [(2084, 2), 4053, 34]-NRT-code) | [i] | OOA Folding | |