Information on Result #1712080
Digital (212, 246, 1250)-net over F2, using net defined by OOA based on linear OOA(2246, 1250, F2, 42, 34) (dual of [(1250, 42), 52254, 35]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(2246, 3751, F2, 6, 34) (dual of [(3751, 6), 22260, 35]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2246, 3752, F2, 6, 34) (dual of [(3752, 6), 22266, 35]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2246, 3752, F2, 4, 34) (dual of [(3752, 4), 14762, 35]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2246, 4104, F2, 4, 34) (dual of [(4104, 4), 16170, 35]-NRT-code), using
- 1 step truncation [i] based on linear OOA(2247, 4105, F2, 4, 35) (dual of [(4105, 4), 16173, 36]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2247, 16420, F2, 35) (dual of [16420, 16173, 36]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2246, 16419, F2, 35) (dual of [16419, 16173, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(30) [i] based on
- linear OA(2239, 16384, F2, 35) (dual of [16384, 16145, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(2211, 16384, F2, 31) (dual of [16384, 16173, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(27, 35, F2, 3) (dual of [35, 28, 4]-code or 35-cap in PG(6,2)), using
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 4 [i]
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- construction X applied to Ce(34) ⊂ Ce(30) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(2246, 16419, F2, 35) (dual of [16419, 16173, 36]-code), using
- OOA 4-folding [i] based on linear OA(2247, 16420, F2, 35) (dual of [16420, 16173, 36]-code), using
- 1 step truncation [i] based on linear OOA(2247, 4105, F2, 4, 35) (dual of [(4105, 4), 16173, 36]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2246, 4104, F2, 4, 34) (dual of [(4104, 4), 16170, 35]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2246, 3752, F2, 4, 34) (dual of [(3752, 4), 14762, 35]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2246, 3752, F2, 6, 34) (dual of [(3752, 6), 22266, 35]-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.