Information on Result #1710904
Digital (155, 180, 1836)-net over F2, using net defined by OOA based on linear OOA(2180, 1836, F2, 30, 25) (dual of [(1836, 30), 54900, 26]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(2180, 3673, F2, 6, 25) (dual of [(3673, 6), 21858, 26]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2180, 3673, F2, 4, 25) (dual of [(3673, 4), 14512, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2180, 4106, F2, 4, 25) (dual of [(4106, 4), 16244, 26]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2176, 4105, F2, 4, 25) (dual of [(4105, 4), 16244, 26]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2176, 16420, F2, 25) (dual of [16420, 16244, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- linear OA(2169, 16385, F2, 25) (dual of [16385, 16216, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 228−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(2141, 16385, F2, 21) (dual of [16385, 16244, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 228−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [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 C([0,12]) ⊂ C([0,10]) [i] based on
- OOA 4-folding [i] based on linear OA(2176, 16420, F2, 25) (dual of [16420, 16244, 26]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2176, 4105, F2, 4, 25) (dual of [(4105, 4), 16244, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2180, 4106, F2, 4, 25) (dual of [(4106, 4), 16244, 26]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2180, 3673, F2, 4, 25) (dual of [(3673, 4), 14512, 26]-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.