Information on Result #1775495
Digital (115, 132, 524314)-net over F4, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(4132, 524314, F4, 2, 17) (dual of [(524314, 2), 1048496, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4132, 1048628, F4, 17) (dual of [1048628, 1048496, 18]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4131, 1048627, F4, 17) (dual of [1048627, 1048496, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,5]) [i] based on
- linear OA(4121, 1048577, F4, 17) (dual of [1048577, 1048456, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 420−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(481, 1048577, F4, 11) (dual of [1048577, 1048496, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 420−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(410, 50, F4, 5) (dual of [50, 40, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- construction X applied to C([0,8]) ⊂ C([0,5]) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4131, 1048627, F4, 17) (dual of [1048627, 1048496, 18]-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.