Information on Result #701400
Linear OA(741, 68, F7, 21) (dual of [68, 27, 22]-code), using construction XX applied to C1 = C({1,2,5,6,8,9,10,11,12,13,16,17,18,19,20}), C2 = C([0,16]), C3 = C1 + C2 = C({1,2,5,6,8,9,10,11,12,13,16}), and C∩ = C1 ∩ C2 = C([0,20]) based on
- linear OA(728, 48, F7, 16) (dual of [48, 20, 17]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {1,2,5,6,8,9,10,11,12,13,16,17,18,19,20}, and minimum distance d ≥ |{5,6,…,20}|+1 = 17 (BCH-bound) [i]
- linear OA(725, 48, F7, 17) (dual of [48, 23, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(733, 48, F7, 24) (dual of [48, 15, 25]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(720, 48, F7, 12) (dual of [48, 28, 13]-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}, and minimum distance d ≥ |{5,6,…,16}|+1 = 13 (BCH-bound) [i]
- linear OA(74, 12, F7, 3) (dual of [12, 8, 4]-code or 12-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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(741, 34, F7, 2, 21) (dual of [(34, 2), 27, 22]-NRT-code) | [i] | OOA Folding | |