Information on Result #686015
Linear OA(746, 67, F7, 25) (dual of [67, 21, 26]-code), using construction XX applied to C1 = C([0,18]), C2 = C([1,22]), C3 = C1 + C2 = C([1,18]), and C∩ = C1 ∩ C2 = C([0,22]) based on
- linear OA(737, 57, F7, 21) (dual of [57, 20, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 57 | 73−1, defining interval I = [0,18], and minimum distance d ≥ |{−2,−1,…,18}|+1 = 22 (BCH-bound) [i]
- linear OA(740, 57, F7, 22) (dual of [57, 17, 23]-code), using the narrow-sense BCH-code C(I) with length 57 | 73−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(741, 57, F7, 25) (dual of [57, 16, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 57 | 73−1, defining interval I = [0,22], and minimum distance d ≥ |{−2,−1,…,22}|+1 = 26 (BCH-bound) [i]
- linear OA(736, 57, F7, 18) (dual of [57, 21, 19]-code), using the narrow-sense BCH-code C(I) with length 57 | 73−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(72, 3, F7, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,7)), using
- dual of repetition code with length 3 [i]
- linear OA(73, 7, F7, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,7) or 7-cap in PG(2,7)), using
- Reed–Solomon code RS(4,7) [i]
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.