Information on Result #1722732
Digital (67, 83, 5220)-net over F5, using net defined by OOA based on linear OOA(583, 5220, F5, 21, 16) (dual of [(5220, 21), 109537, 17]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(583, 15661, F5, 3, 16) (dual of [(15661, 3), 46900, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(583, 15662, F5, 3, 16) (dual of [(15662, 3), 46903, 17]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(583, 15662, F5, 16) (dual of [15662, 15579, 17]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(579, 15655, F5, 16) (dual of [15655, 15576, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- linear OA(573, 15625, F5, 16) (dual of [15625, 15552, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(549, 15625, F5, 11) (dual of [15625, 15576, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(56, 30, F5, 4) (dual of [30, 24, 5]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- linear OA(579, 15658, F5, 14) (dual of [15658, 15579, 15]-code), using Gilbert–Varšamov bound and bm = 579 > Vbs−1(k−1) = 36444 905124 286882 983875 522980 917687 265790 301589 341925 [i]
- linear OA(51, 4, F5, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(579, 15655, F5, 16) (dual of [15655, 15576, 17]-code), using
- construction X with Varšamov bound [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(583, 15662, F5, 16) (dual of [15662, 15579, 17]-code), using
- discarding factors / shortening the dual code based on linear OOA(583, 15662, F5, 3, 16) (dual of [(15662, 3), 46903, 17]-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.