Information on Result #680918
Linear OA(4209, 1097, F4, 49) (dual of [1097, 888, 50]-code), using construction X applied to Ce(48) ⊂ Ce(36) based on
- linear OA(4181, 1024, F4, 49) (dual of [1024, 843, 50]-code), using an extension Ce(48) of the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,48], and designed minimum distance d ≥ |I|+1 = 49 [i]
- linear OA(4136, 1024, F4, 37) (dual of [1024, 888, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(428, 73, F4, 11) (dual of [73, 45, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(428, 76, F4, 11) (dual of [76, 48, 12]-code), using
- trace code [i] based on linear OA(1614, 38, F16, 11) (dual of [38, 24, 12]-code), using
- extended algebraic-geometric code AGe(F,26P) [i] based on function field F/F16 with g(F) = 3 and N(F) ≥ 38, using
- trace code [i] based on linear OA(1614, 38, F16, 11) (dual of [38, 24, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(428, 76, F4, 11) (dual of [76, 48, 12]-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(4209, 1097, F4, 48) (dual of [1097, 888, 49]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(4208, 1096, F4, 48) (dual of [1096, 888, 49]-code) | [i] | Truncation | |