Information on Result #1773564
Digital (73, 84, 524301)-net over F4, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(484, 524301, F4, 2, 11) (dual of [(524301, 2), 1048518, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(484, 1048602, F4, 11) (dual of [1048602, 1048518, 12]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(482, 1048599, F4, 11) (dual of [1048599, 1048517, 12]-code), using
- construction X4 applied to C([0,5]) ⊂ C([0,4]) [i] based on
- linear OA(481, 1048577, F4, 11) (dual of [1048577, 1048496, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 420−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(461, 1048577, F4, 9) (dual of [1048577, 1048516, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 420−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [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 C([0,5]) ⊂ C([0,4]) [i] based on
- linear OA(482, 1048600, F4, 9) (dual of [1048600, 1048518, 10]-code), using Gilbert–Varšamov bound and bm = 482 > Vbs−1(k−1) = 237856 232576 187549 974856 024211 765017 061338 727546 [i]
- linear OA(41, 2, F4, 1) (dual of [2, 1, 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 (see above)
- linear OA(482, 1048599, F4, 11) (dual of [1048599, 1048517, 12]-code), using
- construction X with Varšamov bound [i] based on
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.