Information on Result #701396
Linear OA(738, 66, F7, 20) (dual of [66, 28, 21]-code), using construction XX applied to C1 = C({1,2,5,6,8,9,10,11,12,13,16,17,18,19}), C2 = C([0,16]), C3 = C1 + C2 = C({1,2,5,6,8,9,10,11,12,13,16}), and C∩ = C1 ∩ C2 = C([0,19]) based on
- linear OA(726, 48, F7, 15) (dual of [48, 22, 16]-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}, and minimum distance d ≥ |{5,6,…,19}|+1 = 16 (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(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(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, 10, F7, 4) (dual of [10, 5, 5]-code), using
- discarding factors / shortening the dual code based on 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
- discarding factors / shortening the dual code based on linear OA(75, 11, F7, 4) (dual of [11, 6, 5]-code), 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(738, 33, F7, 2, 20) (dual of [(33, 2), 28, 21]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(738, 22, F7, 3, 20) (dual of [(22, 3), 28, 21]-NRT-code) | [i] | ||