Information on Result #692407
Linear OA(16109, 4150, F16, 33) (dual of [4150, 4041, 34]-code), using construction X applied to Ce(32) ⊂ Ce(19) 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(1655, 4096, F16, 20) (dual of [4096, 4041, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(1618, 54, F16, 12) (dual of [54, 36, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(1618, 64, F16, 12) (dual of [64, 46, 13]-code), using
- algebraic-geometric code AG(F,51P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- algebraic-geometric code AG(F,51P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- discarding factors / shortening the dual code based on linear OA(1618, 64, F16, 12) (dual of [64, 46, 13]-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 OA(16108, 4149, F16, 32) (dual of [4149, 4041, 33]-code) | [i] | Truncation | |
| 2 | Linear OOA(16109, 2075, F16, 2, 33) (dual of [(2075, 2), 4041, 34]-NRT-code) | [i] | OOA Folding | |