Information on Result #700615
Linear OA(284, 151, F2, 24) (dual of [151, 67, 25]-code), using construction XX applied to C1 = C({0,1,3,5,7,9,11,13,15,31,63}), C2 = C([1,19]), C3 = C1 + C2 = C([1,15]), and C∩ = C1 ∩ C2 = C({0,1,3,5,7,9,11,13,15,19,31,63}) based on
- linear OA(271, 127, F2, 23) (dual of [127, 56, 24]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,11,13,15,31,63}, and minimum distance d ≥ |{−4,−3,…,18}|+1 = 24 (BCH-bound) [i]
- linear OA(263, 127, F2, 20) (dual of [127, 64, 21]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(278, 127, F2, 25) (dual of [127, 49, 26]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,11,13,15,19,31,63}, and minimum distance d ≥ |{−4,−3,…,20}|+1 = 26 (BCH-bound) [i]
- linear OA(256, 127, F2, 18) (dual of [127, 71, 19]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(25, 16, F2, 3) (dual of [16, 11, 4]-code or 16-cap in PG(4,2)), using
- linear OA(21, 8, F2, 1) (dual of [8, 7, 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
Mode: Constructive and 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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
None.