Information on Result #1789545
Digital (22, 27, 235306)-net over F7, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(727, 235306, F7, 5) (dual of [235306, 235279, 6]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(726, 235304, F7, 5) (dual of [235304, 235278, 6]-code), using
- trace code [i] based on linear OA(4913, 117652, F49, 5) (dual of [117652, 117639, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(4913, 117649, F49, 5) (dual of [117649, 117636, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(4910, 117649, F49, 4) (dual of [117649, 117639, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(490, 3, F49, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- trace code [i] based on linear OA(4913, 117652, F49, 5) (dual of [117652, 117639, 6]-code), using
- linear OA(726, 235305, F7, 4) (dual of [235305, 235279, 5]-code), using Gilbert–Varšamov bound and bm = 726 > Vbs−1(k−1) = 469014 010626 081505 [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(726, 235304, F7, 5) (dual of [235304, 235278, 6]-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.