Information on Result #1304043
Linear OA(2257, 578, F2, 56) (dual of [578, 321, 57]-code), using 27 step Varšamov–Edel lengthening with (ri) = (5, 3, 2, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0) based on linear OA(2236, 530, F2, 56) (dual of [530, 294, 57]-code), using
- 1 times truncation [i] based on linear OA(2237, 531, F2, 57) (dual of [531, 294, 58]-code), using
- construction XX applied to C1 = C([509,52]), C2 = C([0,54]), C3 = C1 + C2 = C([0,52]), and C∩ = C1 ∩ C2 = C([509,54]) [i] based on
- linear OA(2226, 511, F2, 55) (dual of [511, 285, 56]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,52}, and designed minimum distance d ≥ |I|+1 = 56 [i]
- linear OA(2226, 511, F2, 55) (dual of [511, 285, 56]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,54], and designed minimum distance d ≥ |I|+1 = 56 [i]
- linear OA(2235, 511, F2, 57) (dual of [511, 276, 58]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,54}, and designed minimum distance d ≥ |I|+1 = 58 [i]
- linear OA(2217, 511, F2, 53) (dual of [511, 294, 54]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,52], and designed minimum distance d ≥ |I|+1 = 54 [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
- linear OA(21, 10, F2, 1) (dual of [10, 9, 2]-code) (see above)
- construction XX applied to C1 = C([509,52]), C2 = C([0,54]), C3 = C1 + C2 = C([0,52]), and C∩ = C1 ∩ C2 = C([509,54]) [i] based on
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.