Information on Result #1727266
Digital (63, 75, 1048588)-net over F8, using net defined by OOA based on linear OOA(875, 1048588, F8, 15, 12) (dual of [(1048588, 15), 15728745, 13]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(875, 2097177, F8, 3, 12) (dual of [(2097177, 3), 6291456, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(875, 2097178, F8, 3, 12) (dual of [(2097178, 3), 6291459, 13]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(875, 2097178, F8, 12) (dual of [2097178, 2097103, 13]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(874, 2097176, F8, 12) (dual of [2097176, 2097102, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- linear OA(871, 2097152, F8, 12) (dual of [2097152, 2097081, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(850, 2097152, F8, 9) (dual of [2097152, 2097102, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(83, 24, F8, 2) (dual of [24, 21, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- linear OA(874, 2097177, F8, 11) (dual of [2097177, 2097103, 12]-code), using Gilbert–Varšamov bound and bm = 874 > Vbs−1(k−1) = 128102 361101 264540 908329 698815 640863 772881 568097 645042 242732 791298 [i]
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(874, 2097176, F8, 12) (dual of [2097176, 2097102, 13]-code), using
- construction X with Varšamov bound [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(875, 2097178, F8, 12) (dual of [2097178, 2097103, 13]-code), using
- discarding factors / shortening the dual code based on linear OOA(875, 2097178, F8, 3, 12) (dual of [(2097178, 3), 6291459, 13]-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.