Information on Result #1708744
Digital (45, 58, 205)-net over F2, using net defined by OOA based on linear OOA(258, 205, F2, 18, 13) (dual of [(205, 18), 3632, 14]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(258, 206, F2, 6, 13) (dual of [(206, 6), 1178, 14]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(258, 206, F2, 2, 13) (dual of [(206, 2), 354, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(258, 266, F2, 2, 13) (dual of [(266, 2), 474, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(258, 532, F2, 13) (dual of [532, 474, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(258, 533, F2, 13) (dual of [533, 475, 14]-code), using
- adding a parity check bit [i] based on linear OA(257, 532, F2, 12) (dual of [532, 475, 13]-code), using
- construction XX applied to C1 = C([509,8]), C2 = C([1,10]), C3 = C1 + C2 = C([1,8]), and C∩ = C1 ∩ C2 = C([509,10]) [i] based on
- linear OA(246, 511, F2, 11) (dual of [511, 465, 12]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,8}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(245, 511, F2, 10) (dual of [511, 466, 11]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(255, 511, F2, 13) (dual of [511, 456, 14]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,10}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(236, 511, F2, 8) (dual of [511, 475, 9]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(21, 11, F2, 1) (dual of [11, 10, 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, 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 (see above)
- construction XX applied to C1 = C([509,8]), C2 = C([1,10]), C3 = C1 + C2 = C([1,8]), and C∩ = C1 ∩ C2 = C([509,10]) [i] based on
- adding a parity check bit [i] based on linear OA(257, 532, F2, 12) (dual of [532, 475, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(258, 533, F2, 13) (dual of [533, 475, 14]-code), using
- OOA 2-folding [i] based on linear OA(258, 532, F2, 13) (dual of [532, 474, 14]-code), using
- discarding factors / shortening the dual code based on linear OOA(258, 266, F2, 2, 13) (dual of [(266, 2), 474, 14]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(258, 206, F2, 2, 13) (dual of [(206, 2), 354, 14]-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.