Information on Result #1749133
Digital (40, 53, 138)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(253, 138, F2, 2, 13) (dual of [(138, 2), 223, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(253, 276, F2, 13) (dual of [276, 223, 14]-code), using
- 1 times code embedding in larger space [i] based on linear OA(252, 275, F2, 13) (dual of [275, 223, 14]-code), using
- adding a parity check bit [i] based on linear OA(251, 274, F2, 12) (dual of [274, 223, 13]-code), using
- construction XX applied to C1 = C([253,8]), C2 = C([1,10]), C3 = C1 + C2 = C([1,8]), and C∩ = C1 ∩ C2 = C([253,10]) [i] based on
- linear OA(241, 255, F2, 11) (dual of [255, 214, 12]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,8}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(240, 255, F2, 10) (dual of [255, 215, 11]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(249, 255, F2, 13) (dual of [255, 206, 14]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,10}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(232, 255, F2, 8) (dual of [255, 223, 9]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(21, 10, F2, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(21, 9, F2, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s (see above)
- construction XX applied to C1 = C([253,8]), C2 = C([1,10]), C3 = C1 + C2 = C([1,8]), and C∩ = C1 ∩ C2 = C([253,10]) [i] based on
- adding a parity check bit [i] based on linear OA(251, 274, F2, 12) (dual of [274, 223, 13]-code), using
- 1 times code embedding in larger space [i] based on linear OA(252, 275, F2, 13) (dual of [275, 223, 14]-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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (41, 54, 138)-net over F2 | [i] | Net Duplication | |