Information on Result #1489425
Linear OOA(881, 4102, F8, 3, 20) (dual of [(4102, 3), 12225, 21]-NRT-code), using OOA 2-folding based on linear OOA(881, 8204, F8, 2, 20) (dual of [(8204, 2), 16327, 21]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(881, 8204, F8, 20) (dual of [8204, 8123, 21]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(880, 8202, F8, 20) (dual of [8202, 8122, 21]-code), using
- trace code [i] based on linear OA(6440, 4101, F64, 20) (dual of [4101, 4061, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(17) [i] based on
- linear OA(6439, 4096, F64, 20) (dual of [4096, 4057, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(6435, 4096, F64, 18) (dual of [4096, 4061, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(641, 5, F64, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(19) ⊂ Ce(17) [i] based on
- trace code [i] based on linear OA(6440, 4101, F64, 20) (dual of [4101, 4061, 21]-code), using
- linear OA(880, 8203, F8, 19) (dual of [8203, 8123, 20]-code), using Gilbert–Varšamov bound and bm = 880 > Vbs−1(k−1) = 7047 074069 270492 436962 796921 310817 287746 933217 522399 873928 533030 426624 [i]
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(880, 8202, F8, 20) (dual of [8202, 8122, 21]-code), using
- construction X with Varšamov bound [i] based on
Mode: 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
None.