Information on Result #1799983
Digital (98, 131, 13128)-net over F9, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(9131, 13128, F9, 33) (dual of [13128, 12997, 34]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(9130, 13126, F9, 33) (dual of [13126, 12996, 34]-code), using
- trace code [i] based on linear OA(8165, 6563, F81, 33) (dual of [6563, 6498, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(31) [i] based on
- linear OA(8165, 6561, F81, 33) (dual of [6561, 6496, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(8163, 6561, F81, 32) (dual of [6561, 6498, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(810, 2, F81, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(32) ⊂ Ce(31) [i] based on
- trace code [i] based on linear OA(8165, 6563, F81, 33) (dual of [6563, 6498, 34]-code), using
- linear OA(9130, 13127, F9, 32) (dual of [13127, 12997, 33]-code), using Gilbert–Varšamov bound and bm = 9130 > Vbs−1(k−1) = 53 407660 739261 997504 274970 375037 969563 571616 059301 421379 604995 101040 737510 936890 862782 721517 617809 435619 020509 039557 389809 [i]
- linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(9130, 13126, F9, 33) (dual of [13126, 12996, 34]-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.