Information on Result #1719382
Digital (130, 155, 8437)-net over F4, using net defined by OOA based on linear OOA(4155, 8437, F4, 27, 25) (dual of [(8437, 27), 227644, 26]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(4155, 33749, F4, 3, 25) (dual of [(33749, 3), 101092, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4155, 33751, F4, 3, 25) (dual of [(33751, 3), 101098, 26]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4155, 33751, F4, 25) (dual of [33751, 33596, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4155, 65579, F4, 25) (dual of [65579, 65424, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- linear OA(4145, 65537, F4, 25) (dual of [65537, 65392, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(4113, 65537, F4, 19) (dual of [65537, 65424, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(410, 42, F4, 5) (dual of [42, 32, 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(4155, 65579, F4, 25) (dual of [65579, 65424, 26]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4155, 33751, F4, 25) (dual of [33751, 33596, 26]-code), using
- discarding factors / shortening the dual code based on linear OOA(4155, 33751, F4, 3, 25) (dual of [(33751, 3), 101098, 26]-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.