Information on Result #701386
Linear OA(734, 64, F7, 18) (dual of [64, 30, 19]-code), using construction XX applied to C1 = C({0,1,2,3,4,5,6,8,9,10,34,41}), C2 = C([0,13]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C({0,1,2,3,4,5,6,8,9,10,11,12,13,34,41}) based on
- linear OA(722, 48, F7, 13) (dual of [48, 26, 14]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {0,1,2,3,4,5,6,8,9,10,34,41}, and minimum distance d ≥ |{−2,−1,…,10}|+1 = 14 (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(728, 48, F7, 18) (dual of [48, 20, 19]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {0,1,2,3,4,5,6,8,9,10,11,12,13,34,41}, and minimum distance d ≥ |{−2,−1,…,15}|+1 = 19 (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(71, 5, F7, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, 7, F7, 1) (dual of [7, 6, 2]-code), using
- Reed–Solomon code RS(6,7) [i]
- discarding factors / shortening the dual code based on linear OA(71, 7, F7, 1) (dual of [7, 6, 2]-code), using
- 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, using the rational function field F7(x) [i]
- 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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(734, 32, F7, 2, 18) (dual of [(32, 2), 30, 19]-NRT-code) | [i] | OOA Folding | |