Information on Result #1722988
Digital (54, 72, 712)-net over F5, using net defined by OOA based on linear OOA(572, 712, F5, 21, 18) (dual of [(712, 21), 14880, 19]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(572, 2137, F5, 3, 18) (dual of [(2137, 3), 6339, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(572, 2138, F5, 3, 18) (dual of [(2138, 3), 6342, 19]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(572, 2138, F5, 18) (dual of [2138, 2066, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(572, 3136, F5, 18) (dual of [3136, 3064, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(15) [i] based on
- linear OA(571, 3125, F5, 18) (dual of [3125, 3054, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(561, 3125, F5, 16) (dual of [3125, 3064, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(51, 11, F5, 1) (dual of [11, 10, 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
- construction X applied to Ce(17) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(572, 3136, F5, 18) (dual of [3136, 3064, 19]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(572, 2138, F5, 18) (dual of [2138, 2066, 19]-code), using
- discarding factors / shortening the dual code based on linear OOA(572, 2138, F5, 3, 18) (dual of [(2138, 3), 6342, 19]-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.