Information on Result #1781811
Digital (183, 223, 16433)-net over F4, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4223, 16433, F4, 40) (dual of [16433, 16210, 41]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4220, 16428, F4, 40) (dual of [16428, 16208, 41]-code), using
- construction X applied to Ce(40) ⊂ Ce(33) [i] based on
- linear OA(4211, 16384, F4, 41) (dual of [16384, 16173, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(4176, 16384, F4, 34) (dual of [16384, 16208, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(49, 44, F4, 5) (dual of [44, 35, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(49, 51, F4, 5) (dual of [51, 42, 6]-code), using
- a “DaH†code from Brouwer’s database [i]
- discarding factors / shortening the dual code based on linear OA(49, 51, F4, 5) (dual of [51, 42, 6]-code), using
- construction X applied to Ce(40) ⊂ Ce(33) [i] based on
- linear OA(4220, 16430, F4, 38) (dual of [16430, 16210, 39]-code), using Gilbert–Varšamov bound and bm = 4220 > Vbs−1(k−1) = 29858 617316 313925 591607 719692 708220 547096 826525 437527 811578 734306 021120 465026 309411 934242 775566 809740 637002 109302 382758 232533 569392 [i]
- linear OA(41, 3, F4, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(4220, 16428, F4, 40) (dual of [16428, 16208, 41]-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.