Information on Result #701388
Linear OA(737, 67, F7, 19) (dual of [67, 30, 20]-code), using construction XX applied to C1 = C({0,1,2,3,4,5,6,8,9,10,27,34,41}), C2 = C([0,13]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C({0,1,2,3,4,5,6,8,9,10,11,12,13,27,34,41}) based on
- linear OA(724, 48, F7, 14) (dual of [48, 24, 15]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {0,1,2,3,4,5,6,8,9,10,27,34,41}, and minimum distance d ≥ |{−3,−2,…,10}|+1 = 15 (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(730, 48, F7, 19) (dual of [48, 18, 20]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {0,1,2,3,4,5,6,8,9,10,11,12,13,27,34,41}, and minimum distance d ≥ |{−3,−2,…,15}|+1 = 20 (BCH-bound) [i]
- linear OA(718, 48, F7, 11) (dual of [48, 30, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(72, 8, F7, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,7)), using
- extended Reed–Solomon code RSe(6,7) [i]
- Hamming code H(2,7) [i]
- algebraic-geometric code AG(F, Q+1P) 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]
- linear OA(75, 11, F7, 4) (dual of [11, 6, 5]-code), using
- construction X applied to AG(F, Q+0P) ⊂ AG(F, Q+1P) [i] based on
- linear OA(74, 8, F7, 4) (dual of [8, 4, 5]-code or 8-arc in PG(3,7)), using 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 (see above)
- linear OA(72, 8, F7, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,7)), using algebraic-geometric code AG(F, Q+1P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F7 with g(F) = 0 and N(F) ≥ 8 (see above)
- linear OA(71, 3, F7, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to AG(F, Q+0P) ⊂ AG(F, Q+1P) [i] based on
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.