Information on Result #1807391
Digital (63, 93, 19713)-net over F27, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(2793, 19713, F27, 30) (dual of [19713, 19620, 31]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(2792, 19711, F27, 30) (dual of [19711, 19619, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(21) [i] based on
- linear OA(2785, 19683, F27, 30) (dual of [19683, 19598, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(2764, 19683, F27, 22) (dual of [19683, 19619, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(277, 28, F27, 7) (dual of [28, 21, 8]-code or 28-arc in PG(6,27)), using
- extended Reed–Solomon code RSe(21,27) [i]
- the expurgated narrow-sense BCH-code C(I) with length 28 | 272−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- construction X applied to Ce(29) ⊂ Ce(21) [i] based on
- linear OA(2792, 19712, F27, 29) (dual of [19712, 19620, 30]-code), using Gilbert–Varšamov bound and bm = 2792 > Vbs−1(k−1) = 23913 696642 876181 423233 841026 328187 071540 992826 960651 191865 418059 955347 305690 456487 235153 323393 383536 560152 151905 500098 514082 536979 [i]
- linear OA(270, 1, F27, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(2792, 19711, F27, 30) (dual of [19711, 19619, 31]-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.