Information on Result #1756323
Digital (198, 214, 2097228)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2214, 2097228, F2, 4, 16) (dual of [(2097228, 4), 8388698, 17]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(230, 78, F2, 4, 8) (dual of [(78, 4), 282, 9]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(230, 78, F2, 8) (dual of [78, 48, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(230, 137, F2, 8) (dual of [137, 107, 9]-code), using
- construction X4 applied to C([0,8]) ⊂ C([1,6]) [i] based on
- linear OA(229, 127, F2, 9) (dual of [127, 98, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(221, 127, F2, 6) (dual of [127, 106, 7]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(29, 10, F2, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,2)), using
- dual of repetition code with length 10 [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
- construction X4 applied to C([0,8]) ⊂ C([1,6]) [i] based on
- discarding factors / shortening the dual code based on linear OA(230, 137, F2, 8) (dual of [137, 107, 9]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(230, 78, F2, 8) (dual of [78, 48, 9]-code), using
- linear OOA(2184, 2097150, F2, 4, 16) (dual of [(2097150, 4), 8388416, 17]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2184, 8388600, F2, 16) (dual of [8388600, 8388416, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2184, large, F2, 16) (dual of [large, large−184, 17]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(2184, large, F2, 16) (dual of [large, large−184, 17]-code), using
- OOA 4-folding [i] based on linear OA(2184, 8388600, F2, 16) (dual of [8388600, 8388416, 17]-code), using
- linear OOA(230, 78, F2, 4, 8) (dual of [(78, 4), 282, 9]-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.