Information on Result #1780057
Digital (179, 202, 2097187)-net over F4, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(4202, 2097187, F4, 2, 23) (dual of [(2097187, 2), 4194172, 24]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4202, 4194374, F4, 23) (dual of [4194374, 4194172, 24]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4198, 4194368, F4, 23) (dual of [4194368, 4194170, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- linear OA(4188, 4194304, F4, 23) (dual of [4194304, 4194116, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(4133, 4194304, F4, 17) (dual of [4194304, 4194171, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(410, 64, F4, 5) (dual of [64, 54, 6]-code), using
- an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- linear OA(4198, 4194370, F4, 20) (dual of [4194370, 4194172, 21]-code), using Gilbert–Varšamov bound and bm = 4198 > Vbs−1(k−1) = 6469 314011 674311 114816 622408 943640 174727 021127 115634 267470 192158 498997 776757 423473 067170 023195 984452 180848 641166 753044 [i]
- linear OA(42, 4, F4, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,4)), using
- Reed–Solomon code RS(2,4) [i]
- linear OA(4198, 4194368, F4, 23) (dual of [4194368, 4194170, 24]-code), using
- construction X with Varšamov bound [i] based on
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.