Information on Result #1749159
Digital (44, 55, 361)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(255, 361, F2, 2, 11) (dual of [(361, 2), 667, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(255, 524, F2, 2, 11) (dual of [(524, 2), 993, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(255, 1048, F2, 11) (dual of [1048, 993, 12]-code), using
- 1 times code embedding in larger space [i] based on linear OA(254, 1047, F2, 11) (dual of [1047, 993, 12]-code), using
- adding a parity check bit [i] based on linear OA(253, 1046, F2, 10) (dual of [1046, 993, 11]-code), using
- construction XX applied to C1 = C([1021,6]), C2 = C([1,8]), C3 = C1 + C2 = C([1,6]), and C∩ = C1 ∩ C2 = C([1021,8]) [i] based on
- linear OA(241, 1023, F2, 9) (dual of [1023, 982, 10]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,6}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(240, 1023, F2, 8) (dual of [1023, 983, 9]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(251, 1023, F2, 11) (dual of [1023, 972, 12]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,8}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(230, 1023, F2, 6) (dual of [1023, 993, 7]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(21, 12, F2, 1) (dual of [12, 11, 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, 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 (see above)
- construction XX applied to C1 = C([1021,6]), C2 = C([1,8]), C3 = C1 + C2 = C([1,6]), and C∩ = C1 ∩ C2 = C([1021,8]) [i] based on
- adding a parity check bit [i] based on linear OA(253, 1046, F2, 10) (dual of [1046, 993, 11]-code), using
- 1 times code embedding in larger space [i] based on linear OA(254, 1047, F2, 11) (dual of [1047, 993, 12]-code), using
- OOA 2-folding [i] based on linear OA(255, 1048, F2, 11) (dual of [1048, 993, 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.