Information on Result #1722320
Digital (45, 58, 1733)-net over F5, using net defined by OOA based on linear OOA(558, 1733, F5, 15, 13) (dual of [(1733, 15), 25937, 14]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(558, 3467, F5, 3, 13) (dual of [(3467, 3), 10343, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(558, 3468, F5, 3, 13) (dual of [(3468, 3), 10346, 14]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(558, 3468, F5, 13) (dual of [3468, 3410, 14]-code), using
- 331 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 7 times 0, 1, 18 times 0, 1, 41 times 0, 1, 87 times 0, 1, 170 times 0) [i] based on linear OA(551, 3130, F5, 13) (dual of [3130, 3079, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- linear OA(551, 3125, F5, 13) (dual of [3125, 3074, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(546, 3125, F5, 12) (dual of [3125, 3079, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(12) ⊂ Ce(11) [i] based on
- 331 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 7 times 0, 1, 18 times 0, 1, 41 times 0, 1, 87 times 0, 1, 170 times 0) [i] based on linear OA(551, 3130, F5, 13) (dual of [3130, 3079, 14]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(558, 3468, F5, 13) (dual of [3468, 3410, 14]-code), using
- discarding factors / shortening the dual code based on linear OOA(558, 3468, F5, 3, 13) (dual of [(3468, 3), 10346, 14]-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.