Information on Result #1549427
Linear OOA(5116, 1953170, F5, 3, 15) (dual of [(1953170, 3), 5859394, 16]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(5116, 1953170, F5, 15) (dual of [1953170, 1953054, 16]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(5114, 1953167, F5, 15) (dual of [1953167, 1953053, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([0,5]) [i] based on
- linear OA(5109, 1953126, F5, 15) (dual of [1953126, 1953017, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 1953126 | 518−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(573, 1953126, F5, 11) (dual of [1953126, 1953053, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 1953126 | 518−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(55, 41, F5, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,5)), using
- discarding factors / shortening the dual code based on linear OA(55, 42, F5, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,5)), using
- construction X applied to C([0,7]) ⊂ C([0,5]) [i] based on
- linear OA(5114, 1953168, F5, 13) (dual of [1953168, 1953054, 14]-code), using Gilbert–Varšamov bound and bm = 5114 > Vbs−1(k−1) = 107 954676 278300 620272 304741 516008 420354 493324 202169 626192 695764 307318 492045 [i]
- linear OA(51, 2, F5, 1) (dual of [2, 1, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(5114, 1953167, F5, 15) (dual of [1953167, 1953053, 16]-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(5116, 651056, F5, 21, 15) (dual of [(651056, 21), 13672060, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |