Information on Result #701472
Linear OA(744, 65, F7, 26) (dual of [65, 21, 27]-code), using construction XX applied to C1 = C({1,2,3,8,9,10,11,12,13,16,17,18,19,20,24,25}), C2 = C([0,24]), C3 = C1 + C2 = C({1,2,3,8,9,10,11,12,13,16,17,18,19,20,24}), and C∩ = C1 ∩ C2 = C([0,25]) based on
- linear OA(729, 48, F7, 19) (dual of [48, 19, 20]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {1,2,3,8,9,10,11,12,13,16,17,18,19,20,24,25}, and minimum distance d ≥ |{7,8,…,25}|+1 = 20 (BCH-bound) [i]
- linear OA(734, 48, F7, 25) (dual of [48, 14, 26]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,24], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(736, 48, F7, 26) (dual of [48, 12, 27]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,25], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(727, 48, F7, 18) (dual of [48, 21, 19]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {1,2,3,8,9,10,11,12,13,16,17,18,19,20,24}, and minimum distance d ≥ |{7,8,…,24}|+1 = 19 (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, 15, F7, 6) (dual of [15, 7, 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.