Information on Result #1717678
Digital (75, 87, 113638)-net over F4, using net defined by OOA based on linear OOA(487, 113638, F4, 15, 12) (dual of [(113638, 15), 1704483, 13]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(487, 227277, F4, 3, 12) (dual of [(227277, 3), 681744, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(487, 227278, F4, 3, 12) (dual of [(227278, 3), 681747, 13]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(487, 227278, F4, 12) (dual of [227278, 227191, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(487, 262176, F4, 12) (dual of [262176, 262089, 13]-code), using
- strength reduction [i] based on linear OA(487, 262176, F4, 13) (dual of [262176, 262089, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(8) [i] based on
- linear OA(482, 262144, F4, 13) (dual of [262144, 262062, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(455, 262144, F4, 9) (dual of [262144, 262089, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(45, 32, F4, 3) (dual of [32, 27, 4]-code or 32-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- construction X applied to Ce(12) ⊂ Ce(8) [i] based on
- strength reduction [i] based on linear OA(487, 262176, F4, 13) (dual of [262176, 262089, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(487, 262176, F4, 12) (dual of [262176, 262089, 13]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(487, 227278, F4, 12) (dual of [227278, 227191, 13]-code), using
- discarding factors / shortening the dual code based on linear OOA(487, 227278, F4, 3, 12) (dual of [(227278, 3), 681747, 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.