Information on Result #701390
Linear OA(735, 67, F7, 18) (dual of [67, 32, 19]-code), using construction XX applied to C1 = C({1,2,8,9,10,11,12,13,16,17}), C2 = C([0,16]), C3 = C1 + C2 = C({1,2,8,9,10,11,12,13,16}), and C∩ = C1 ∩ C2 = C([0,17]) based on
- linear OA(718, 48, F7, 11) (dual of [48, 30, 12]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {1,2,8,9,10,11,12,13,16,17}, and minimum distance d ≥ |{7,8,…,17}|+1 = 12 (BCH-bound) [i]
- linear OA(725, 48, F7, 17) (dual of [48, 23, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(727, 48, F7, 18) (dual of [48, 21, 19]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(716, 48, F7, 10) (dual of [48, 32, 11]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {1,2,8,9,10,11,12,13,16}, and minimum distance d ≥ |{7,8,…,16}|+1 = 11 (BCH-bound) [i]
- linear OA(70, 2, F7, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(78, 17, F7, 6) (dual of [17, 9, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(78, 19, F7, 6) (dual of [19, 11, 7]-code), 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.