Information on Result #1725082
Digital (48, 59, 58835)-net over F7, using net defined by OOA based on linear OOA(759, 58835, F7, 15, 11) (dual of [(58835, 15), 882466, 12]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(759, 117671, F7, 3, 11) (dual of [(117671, 3), 352954, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(759, 117672, F7, 3, 11) (dual of [(117672, 3), 352957, 12]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(759, 117672, F7, 11) (dual of [117672, 117613, 12]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(758, 117670, F7, 11) (dual of [117670, 117612, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(7) [i] based on
- linear OA(755, 117649, F7, 11) (dual of [117649, 117594, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(737, 117649, F7, 8) (dual of [117649, 117612, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(73, 21, F7, 2) (dual of [21, 18, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(73, 48, F7, 2) (dual of [48, 45, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(73, 48, F7, 2) (dual of [48, 45, 3]-code), using
- construction X applied to Ce(10) ⊂ Ce(7) [i] based on
- linear OA(758, 117671, F7, 10) (dual of [117671, 117613, 11]-code), using Gilbert–Varšamov bound and bm = 758 > Vbs−1(k−1) = 120077 784637 037613 092390 119919 115879 013522 782865 [i]
- linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(758, 117670, F7, 11) (dual of [117670, 117612, 12]-code), using
- construction X with Varšamov bound [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(759, 117672, F7, 11) (dual of [117672, 117613, 12]-code), using
- discarding factors / shortening the dual code based on linear OOA(759, 117672, F7, 3, 11) (dual of [(117672, 3), 352957, 12]-NRT-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.