Information on Result #1554543
Linear OOA(877, 8206, F8, 3, 19) (dual of [(8206, 3), 24541, 20]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(877, 8206, F8, 19) (dual of [8206, 8129, 20]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(876, 8204, F8, 19) (dual of [8204, 8128, 20]-code), using
- trace code [i] based on linear OA(6438, 4102, F64, 19) (dual of [4102, 4064, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- linear OA(6437, 4097, F64, 19) (dual of [4097, 4060, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(6433, 4097, F64, 17) (dual of [4097, 4064, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [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 C([0,9]) ⊂ C([0,8]) [i] based on
- trace code [i] based on linear OA(6438, 4102, F64, 19) (dual of [4102, 4064, 20]-code), using
- linear OA(876, 8205, F8, 18) (dual of [8205, 8129, 19]-code), using Gilbert–Varšamov bound and bm = 876 > Vbs−1(k−1) = 2 223099 089204 329555 148588 464101 294257 019462 533549 831781 618987 926016 [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(876, 8204, F8, 19) (dual of [8204, 8128, 20]-code), using
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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(877, 2735, F8, 21, 19) (dual of [(2735, 21), 57358, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |