Information on Result #735551
Linear OA(12868, 16540, F128, 27) (dual of [16540, 16472, 28]-code), using (u, u+v)-construction based on
- linear OA(12814, 150, F128, 13) (dual of [150, 136, 14]-code), using
- extended algebraic-geometric code AGe(F,136P) [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- linear OA(12854, 16390, F128, 27) (dual of [16390, 16336, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,12]) [i] based on
- linear OA(12853, 16385, F128, 27) (dual of [16385, 16332, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(12849, 16385, F128, 25) (dual of [16385, 16336, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(1281, 5, F128, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,13]) ⊂ C([0,12]) [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 OOA(12868, 8270, F128, 2, 27) (dual of [(8270, 2), 16472, 28]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(12868, 5513, F128, 3, 27) (dual of [(5513, 3), 16471, 28]-NRT-code) | [i] | ||