Information on Result #1707694
Digital (49, 58, 5329)-net over F2, using net defined by OOA based on linear OOA(258, 5329, F2, 9, 9) (dual of [(5329, 9), 47903, 10]-NRT-code), using
- appending kth column [i] based on linear OOA(258, 5329, F2, 8, 9) (dual of [(5329, 8), 42574, 10]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(258, 5329, F2, 3, 9) (dual of [(5329, 3), 15929, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(258, 5466, F2, 3, 9) (dual of [(5466, 3), 16340, 10]-NRT-code), using
- OOA 3-folding [i] based on linear OA(258, 16398, F2, 9) (dual of [16398, 16340, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(258, 16399, F2, 9) (dual of [16399, 16341, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(257, 16384, F2, 9) (dual of [16384, 16327, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(243, 16384, F2, 7) (dual of [16384, 16341, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(21, 15, F2, 1) (dual of [15, 14, 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 X applied to Ce(8) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(258, 16399, F2, 9) (dual of [16399, 16341, 10]-code), using
- OOA 3-folding [i] based on linear OA(258, 16398, F2, 9) (dual of [16398, 16340, 10]-code), using
- discarding factors / shortening the dual code based on linear OOA(258, 5466, F2, 3, 9) (dual of [(5466, 3), 16340, 10]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(258, 5329, F2, 3, 9) (dual of [(5329, 3), 15929, 10]-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.