Information on Result #1719350
Digital (112, 137, 2848)-net over F4, using net defined by OOA based on linear OOA(4137, 2848, F4, 27, 25) (dual of [(2848, 27), 76759, 26]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(4137, 11393, F4, 3, 25) (dual of [(11393, 3), 34042, 26]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4137, 11393, F4, 25) (dual of [11393, 11256, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4137, 16423, F4, 25) (dual of [16423, 16286, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- linear OA(4127, 16385, F4, 25) (dual of [16385, 16258, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(499, 16385, F4, 19) (dual of [16385, 16286, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(410, 38, F4, 5) (dual of [38, 28, 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([0,12]) ⊂ C([0,9]) [i] based on
- discarding factors / shortening the dual code based on linear OA(4137, 16423, F4, 25) (dual of [16423, 16286, 26]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4137, 11393, F4, 25) (dual of [11393, 11256, 26]-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.