Information on Result #1423519
Linear OOA(4144, 16446, F4, 2, 25) (dual of [(16446, 2), 32748, 26]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4144, 16446, F4, 25) (dual of [16446, 16302, 26]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4141, 16441, F4, 25) (dual of [16441, 16300, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,8]) [i] based on
- linear OA(4127, 16385, F4, 25) (dual of [16385, 16258, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(485, 16385, F4, 17) (dual of [16385, 16300, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(414, 56, F4, 7) (dual of [56, 42, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(414, 65, F4, 7) (dual of [65, 51, 8]-code), using
- a “GraXX†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(414, 65, F4, 7) (dual of [65, 51, 8]-code), using
- construction X applied to C([0,12]) ⊂ C([0,8]) [i] based on
- linear OA(4141, 16443, F4, 23) (dual of [16443, 16302, 24]-code), using Gilbert–Varšamov bound and bm = 4141 > Vbs−1(k−1) = 15523 617466 758170 786692 576587 377024 767271 878985 550153 593645 355557 347704 545671 343524 [i]
- linear OA(41, 3, F4, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(4141, 16441, F4, 25) (dual of [16441, 16300, 26]-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(4144, 8223, F4, 3, 25) (dual of [(8223, 3), 24525, 26]-NRT-code) | [i] | OOA Folding | |