Information on Result #692442
Linear OA(16119, 4163, F16, 35) (dual of [4163, 4044, 36]-code), using construction X applied to Ce(34) ⊂ Ce(18) based on
- linear OA(1697, 4096, F16, 35) (dual of [4096, 3999, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(1652, 4096, F16, 19) (dual of [4096, 4044, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(1622, 67, F16, 15) (dual of [67, 45, 16]-code), using
- construction X applied to AG(F,48P) ⊂ AG(F,50P) [i] based on
- linear OA(1621, 64, F16, 15) (dual of [64, 43, 16]-code), using algebraic-geometric code AG(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]
- linear OA(1619, 64, F16, 13) (dual of [64, 45, 14]-code), using algebraic-geometric code AG(F,50P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(161, 3, F16, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(1621, 64, F16, 15) (dual of [64, 43, 16]-code), using algebraic-geometric code AG(F,48P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- construction X applied to AG(F,48P) ⊂ AG(F,50P) [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(16120, 4164, F16, 35) (dual of [4164, 4044, 36]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(16119, 2081, F16, 2, 35) (dual of [(2081, 2), 4043, 36]-NRT-code) | [i] | OOA Folding | |