Information on Result #713694
Linear OA(794, 384, F7, 31) (dual of [384, 290, 32]-code), using construction XX applied to C1 = C([333,18]), C2 = C([0,21]), C3 = C1 + C2 = C([0,18]), and C∩ = C1 ∩ C2 = C([333,21]) based on
- linear OA(773, 342, F7, 28) (dual of [342, 269, 29]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−9,−8,…,18}, and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(755, 342, F7, 22) (dual of [342, 287, 23]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(779, 342, F7, 31) (dual of [342, 263, 32]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−9,−8,…,21}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(749, 342, F7, 19) (dual of [342, 293, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(713, 34, F7, 8) (dual of [34, 21, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(713, 48, F7, 8) (dual of [48, 35, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(713, 48, F7, 8) (dual of [48, 35, 9]-code), using
- 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]
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.
Other Results with Identical Parameters
None.
Depending Results
None.