Information on Result #1749097
Digital (38, 49, 210)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(249, 210, F2, 2, 11) (dual of [(210, 2), 371, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(249, 266, F2, 2, 11) (dual of [(266, 2), 483, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(249, 532, F2, 11) (dual of [532, 483, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(249, 533, F2, 11) (dual of [533, 484, 12]-code), using
- adding a parity check bit [i] based on linear OA(248, 532, F2, 10) (dual of [532, 484, 11]-code), using
- construction XX applied to C1 = C([509,6]), C2 = C([1,8]), C3 = C1 + C2 = C([1,6]), and C∩ = C1 ∩ C2 = C([509,8]) [i] based on
- linear OA(237, 511, F2, 9) (dual of [511, 474, 10]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,6}, and designed minimum distance d ≥ |I|+1 = 10 [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(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(227, 511, F2, 6) (dual of [511, 484, 7]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [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([509,6]), C2 = C([1,8]), C3 = C1 + C2 = C([1,6]), and C∩ = C1 ∩ C2 = C([509,8]) [i] based on
- adding a parity check bit [i] based on linear OA(248, 532, F2, 10) (dual of [532, 484, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(249, 533, F2, 11) (dual of [533, 484, 12]-code), using
- OOA 2-folding [i] based on linear OA(249, 532, F2, 11) (dual of [532, 483, 12]-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.