Information on Result #2295617
Linear OA(2179, 296, F2, 49) (dual of [296, 117, 50]-code), using adding a parity check bit based on linear OA(2178, 295, F2, 48) (dual of [295, 117, 49]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(2172, 287, F2, 48) (dual of [287, 115, 49]-code), using
- construction XX applied to C1 = C([251,42]), C2 = C([1,44]), C3 = C1 + C2 = C([1,42]), and C∩ = C1 ∩ C2 = C([251,44]) [i] based on
- linear OA(2157, 255, F2, 47) (dual of [255, 98, 48]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,42}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(2148, 255, F2, 44) (dual of [255, 107, 45]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(2165, 255, F2, 49) (dual of [255, 90, 50]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,44}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(2140, 255, F2, 42) (dual of [255, 115, 43]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(26, 23, F2, 3) (dual of [23, 17, 4]-code or 23-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- linear OA(21, 9, F2, 1) (dual of [9, 8, 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 XX applied to C1 = C([251,42]), C2 = C([1,44]), C3 = C1 + C2 = C([1,42]), and C∩ = C1 ∩ C2 = C([251,44]) [i] based on
- linear OA(2172, 289, F2, 44) (dual of [289, 117, 45]-code), using Gilbert–Varšamov bound and bm = 2172 > Vbs−1(k−1) = 4183 548251 905052 480260 526675 662160 955527 437426 036264 [i]
- linear OA(24, 6, F2, 3) (dual of [6, 2, 4]-code or 6-cap in PG(3,2)), using
- discarding factors / shortening the dual code based on linear OA(24, 7, F2, 3) (dual of [7, 3, 4]-code or 7-cap in PG(3,2)), using
- Simplex code S(3,2) [i]
- discarding factors / shortening the dual code based on linear OA(24, 7, F2, 3) (dual of [7, 3, 4]-code or 7-cap in PG(3,2)), using
- linear OA(2172, 287, F2, 48) (dual of [287, 115, 49]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
None.