Information on Result #700680
Linear OA(2134, 143, F2, 64) (dual of [143, 9, 65]-code), using construction XX applied to C1 = C({1,3,5,7,9,11,13,15,19,21,23,27,29,31,43,47,63}), C2 = C([1,55]), C3 = C1 + C2 = C([1,47]), and C∩ = C1 ∩ C2 = C([1,63]) based on
- linear OA(2119, 127, F2, 62) (dual of [127, 8, 63]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {1,3,5,7,9,11,13,15,19,21,23,27,29,31,43,47,63}, and minimum distance d ≥ |{9,18,27,…,50}|+1 = 63 (BCH-bound) [i]
- linear OA(2119, 127, F2, 62) (dual of [127, 8, 63]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,55], and designed minimum distance d ≥ |I|+1 = 63 [i]
- linear OA(2126, 127, F2, 126) (dual of [127, 1, 127]-code or 127-arc in PG(125,2)), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,63], and designed minimum distance d ≥ |I|+1 = 127 [i]
- linear OA(2112, 127, F2, 54) (dual of [127, 15, 55]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,47], and designed minimum distance d ≥ |I|+1 = 55 [i]
- linear OA(27, 8, F2, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,2)), using
- dual of repetition code with length 8 [i]
- 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.