Information on Result #1717302
Digital (47, 54, 1048601)-net over F4, using net defined by OOA based on linear OOA(454, 1048601, F4, 9, 7) (dual of [(1048601, 9), 9437355, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(454, 1048602, F4, 3, 7) (dual of [(1048602, 3), 3145752, 8]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(454, 1048602, F4, 7) (dual of [1048602, 1048548, 8]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(452, 1048598, F4, 7) (dual of [1048598, 1048546, 8]-code), using
- construction X4 applied to Ce(6) ⊂ Ce(4) [i] based on
- linear OA(451, 1048576, F4, 7) (dual of [1048576, 1048525, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(431, 1048576, F4, 5) (dual of [1048576, 1048545, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(421, 22, F4, 21) (dual of [22, 1, 22]-code or 22-arc in PG(20,4)), using
- dual of repetition code with length 22 [i]
- linear OA(41, 22, F4, 1) (dual of [22, 21, 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
- construction X4 applied to Ce(6) ⊂ Ce(4) [i] based on
- linear OA(452, 1048600, F4, 6) (dual of [1048600, 1048548, 7]-code), using Gilbert–Varšamov bound and bm = 452 > Vbs−1(k−1) = 2 567253 604063 444960 004641 159678 [i]
- linear OA(40, 2, F4, 0) (dual of [2, 2, 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(452, 1048598, F4, 7) (dual of [1048598, 1048546, 8]-code), using
- construction X with Varšamov bound [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(454, 1048602, F4, 7) (dual of [1048602, 1048548, 8]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.