Information on Result #701379
Linear OA(735, 63, F7, 19) (dual of [63, 28, 20]-code), using construction XX applied to C1 = C({1,2,5,6,8,9,10,11,12,13,16,17,18}), C2 = C([0,13]), C3 = C1 + C2 = C({1,2,5,6,8,9,10,11,12,13}), and C∩ = C1 ∩ C2 = C([0,18]) 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 = {1,2,5,6,8,9,10,11,12,13,16,17,18}, and minimum distance d ≥ |{5,6,…,18}|+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(729, 48, F7, 19) (dual of [48, 19, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [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(72, 7, F7, 2) (dual of [7, 5, 3]-code or 7-arc in PG(1,7)), using
- Reed–Solomon code RS(5,7) [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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(735, 31, F7, 2, 19) (dual of [(31, 2), 27, 20]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(735, 21, F7, 3, 19) (dual of [(21, 3), 28, 20]-NRT-code) | [i] | ||