Information on Result #1421182
Linear OOA(493, 16422, F4, 2, 16) (dual of [(16422, 2), 32751, 17]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(493, 16422, F4, 16) (dual of [16422, 16329, 17]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(492, 16420, F4, 16) (dual of [16420, 16328, 17]-code), using
- construction X applied to C([0,8]) ⊂ C([0,5]) [i] based on
- 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(457, 16385, F4, 11) (dual of [16385, 16328, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(47, 35, F4, 4) (dual of [35, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to C([0,8]) ⊂ C([0,5]) [i] based on
- linear OA(492, 16421, F4, 15) (dual of [16421, 16329, 16]-code), using Gilbert–Varšamov bound and bm = 492 > Vbs−1(k−1) = 5 652354 159452 762794 943295 205529 835421 377288 577081 100392 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(492, 16420, F4, 16) (dual of [16420, 16328, 17]-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(493, 8211, F4, 3, 16) (dual of [(8211, 3), 24540, 17]-NRT-code) | [i] | OOA Folding | |