Information on Result #1722848
Digital (55, 72, 1057)-net over F5, using net defined by OOA based on linear OOA(572, 1057, F5, 21, 17) (dual of [(1057, 21), 22125, 18]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(572, 3172, F5, 3, 17) (dual of [(3172, 3), 9444, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(572, 3173, F5, 3, 17) (dual of [(3173, 3), 9447, 18]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(572, 3173, F5, 17) (dual of [3173, 3101, 18]-code), using
- 37 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 0, 0, 0, 1, 8 times 0, 1, 21 times 0) [i] based on linear OA(566, 3130, F5, 17) (dual of [3130, 3064, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(566, 3125, F5, 17) (dual of [3125, 3059, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(50, 5, F5, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- 37 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 0, 0, 0, 1, 8 times 0, 1, 21 times 0) [i] based on linear OA(566, 3130, F5, 17) (dual of [3130, 3064, 18]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(572, 3173, F5, 17) (dual of [3173, 3101, 18]-code), using
- discarding factors / shortening the dual code based on linear OOA(572, 3173, F5, 3, 17) (dual of [(3173, 3), 9447, 18]-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.