Information on Result #686017
Linear OA(743, 67, F7, 22) (dual of [67, 24, 23]-code), using construction XX applied to C1 = C([0,15]), C2 = C([1,21]), C3 = C1 + C2 = C([1,15]), and C∩ = C1 ∩ C2 = C([0,21]) based on
- linear OA(734, 57, F7, 17) (dual of [57, 23, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 57 | 73−1, defining interval I = [0,15], and minimum distance d ≥ |{−1,0,…,15}|+1 = 18 (BCH-bound) [i]
- linear OA(737, 57, F7, 21) (dual of [57, 20, 22]-code), using the narrow-sense BCH-code C(I) with length 57 | 73−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(738, 57, F7, 24) (dual of [57, 19, 25]-code), using the expurgated narrow-sense BCH-code C(I) with length 57 | 73−1, defining interval I = [0,21], and minimum distance d ≥ |{−2,−1,…,21}|+1 = 25 (BCH-bound) [i]
- linear OA(733, 57, F7, 15) (dual of [57, 24, 16]-code), using the narrow-sense BCH-code C(I) with length 57 | 73−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(71, 2, F7, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- linear OA(74, 8, F7, 4) (dual of [8, 4, 5]-code or 8-arc in PG(3,7)), using
- extended Reed–Solomon code RSe(4,7) [i]
- algebraic-geometric code AG(F, Q+0P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F7 with g(F) = 0 and N(F) ≥ 8, using the rational function field F7(x) [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.