Information on Result #1725886
Digital (63, 81, 5609)-net over F7, using net defined by OOA based on linear OOA(781, 5609, F7, 21, 18) (dual of [(5609, 21), 117708, 19]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(781, 16828, F7, 3, 18) (dual of [(16828, 3), 50403, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(781, 16829, F7, 3, 18) (dual of [(16829, 3), 50406, 19]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(781, 16829, F7, 18) (dual of [16829, 16748, 19]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(779, 16825, F7, 18) (dual of [16825, 16746, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(14) [i] based on
- linear OA(776, 16807, F7, 18) (dual of [16807, 16731, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(761, 16807, F7, 15) (dual of [16807, 16746, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(73, 18, F7, 2) (dual of [18, 15, 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(17) ⊂ Ce(14) [i] based on
- linear OA(779, 16827, F7, 17) (dual of [16827, 16748, 18]-code), using Gilbert–Varšamov bound and bm = 779 > Vbs−1(k−1) = 5 526691 201027 221273 520674 281865 416501 062589 608660 314170 504173 055857 [i]
- linear OA(70, 2, F7, 0) (dual of [2, 2, 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(779, 16825, F7, 18) (dual of [16825, 16746, 19]-code), using
- construction X with Varšamov bound [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(781, 16829, F7, 18) (dual of [16829, 16748, 19]-code), using
- discarding factors / shortening the dual code based on linear OOA(781, 16829, F7, 3, 18) (dual of [(16829, 3), 50406, 19]-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.