Information on Result #701382
Linear OA(739, 67, F7, 20) (dual of [67, 28, 21]-code), using construction XX applied to C1 = C({1,2,5,6,8,9,10,11,12,13,16,17,18,19}), C2 = C([0,13]), C3 = C1 + C2 = C({1,2,5,6,8,9,10,11,12,13}), and C∩ = C1 ∩ C2 = C([0,19]) based on
- linear OA(726, 48, F7, 15) (dual of [48, 22, 16]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {1,2,5,6,8,9,10,11,12,13,16,17,18,19}, and minimum distance d ≥ |{5,6,…,19}|+1 = 16 (BCH-bound) [i]
- linear OA(724, 48, F7, 16) (dual of [48, 24, 17]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(731, 48, F7, 20) (dual of [48, 17, 21]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(719, 48, F7, 11) (dual of [48, 29, 12]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {1,2,5,6,8,9,10,11,12,13}, and minimum distance d ≥ |{5,6,…,15}|+1 = 12 (BCH-bound) [i]
- linear OA(74, 11, F7, 3) (dual of [11, 7, 4]-code or 11-cap in PG(3,7)), using
- 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.