Information on Result #1772588
Digital (31, 36, 4194319)-net over F4, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(436, 4194319, F4, 5) (dual of [4194319, 4194283, 6]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(435, 4194317, F4, 5) (dual of [4194317, 4194282, 6]-code), using
- construction X4 applied to Ce(4) ⊂ Ce(2) [i] based on
- linear OA(434, 4194304, F4, 5) (dual of [4194304, 4194270, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(423, 4194304, F4, 3) (dual of [4194304, 4194281, 4]-code or 4194304-cap in PG(22,4)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(412, 13, F4, 12) (dual of [13, 1, 13]-code or 13-arc in PG(11,4)), using
- dual of repetition code with length 13 [i]
- linear OA(41, 13, F4, 1) (dual of [13, 12, 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 Ce(4) ⊂ Ce(2) [i] based on
- linear OA(435, 4194318, F4, 4) (dual of [4194318, 4194283, 5]-code), using Gilbert–Varšamov bound and bm = 435 > Vbs−1(k−1) = 332 044322 434367 627536 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(435, 4194317, F4, 5) (dual of [4194317, 4194282, 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.