Information on Result #1708482
Digital (41, 53, 153)-net over F2, using net defined by OOA based on linear OOA(253, 153, F2, 18, 12) (dual of [(153, 18), 2701, 13]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(253, 154, F2, 6, 12) (dual of [(154, 6), 871, 13]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(253, 154, F2, 12) (dual of [154, 101, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(253, 276, F2, 12) (dual of [276, 223, 13]-code), using
- 1 times truncation [i] based on linear OA(254, 277, F2, 13) (dual of [277, 223, 14]-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(24, 13, F2, 2) (dual of [13, 9, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(24, 15, F2, 2) (dual of [15, 11, 3]-code), using
- Hamming code H(4,2) [i]
- discarding factors / shortening the dual code based on linear OA(24, 15, F2, 2) (dual of [15, 11, 3]-code), 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, 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
- 1 times truncation [i] based on linear OA(254, 277, F2, 13) (dual of [277, 223, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(253, 276, F2, 12) (dual of [276, 223, 13]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(253, 154, F2, 12) (dual of [154, 101, 13]-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.