Information on Result #691988
Linear OA(16112, 4160, F16, 33) (dual of [4160, 4048, 34]-code), using construction X applied to C([0,16]) ⊂ C([0,8]) based on
- linear OA(1691, 4097, F16, 33) (dual of [4097, 4006, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 166−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(1649, 4097, F16, 17) (dual of [4097, 4048, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 166−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(1621, 63, F16, 15) (dual of [63, 42, 16]-code), using
- discarding factors / shortening the dual code 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]
- algebraic-geometric code AG(F,48P) [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(1621, 64, F16, 15) (dual of [64, 43, 16]-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(16112, 2080, F16, 2, 33) (dual of [(2080, 2), 4048, 34]-NRT-code) | [i] | OOA Folding | |