Information on Result #701399
Linear OA(736, 62, F7, 20) (dual of [62, 26, 21]-code), using construction XX applied to C1 = C({1,2,4,5,6,8,9,10,11,12,13,16,17,18,19}), C2 = C([0,16]), C3 = C1 + C2 = C({1,2,4,5,6,8,9,10,11,12,13,16}), and C∩ = C1 ∩ C2 = C([0,19]) 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 = {1,2,4,5,6,8,9,10,11,12,13,16,17,18,19}, and minimum distance d ≥ |{4,5,…,19}|+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(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(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 = {1,2,4,5,6,8,9,10,11,12,13,16}, and minimum distance d ≥ |{4,5,…,16}|+1 = 14 (BCH-bound) [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(73, 6, F7, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,7) or 6-cap in PG(2,7)), using
- discarding factors / shortening the dual code based on linear OA(73, 7, F7, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,7) or 7-cap in PG(2,7)), using
- Reed–Solomon code RS(4,7) [i]
- discarding factors / shortening the dual code based on linear OA(73, 7, F7, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,7) or 7-cap in PG(2,7)), using
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(736, 31, F7, 2, 20) (dual of [(31, 2), 26, 21]-NRT-code) | [i] | OOA Folding | |