Information on Result #712491
Linear OA(754, 67, F7, 35) (dual of [67, 13, 36]-code), using construction XX applied to C1 = C([8,39]), C2 = C([1,31]), C3 = C1 + C2 = C([8,31]), and C∩ = C1 ∩ C2 = C([1,39]) based on
- linear OA(740, 48, F7, 32) (dual of [48, 8, 33]-code), using the primitive BCH-code C(I) with length 48 = 72−1, defining interval I = {8,9,…,39}, and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(739, 48, F7, 31) (dual of [48, 9, 32]-code), using the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(744, 48, F7, 39) (dual of [48, 4, 40]-code), using the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(733, 48, F7, 24) (dual of [48, 15, 25]-code), using the primitive BCH-code C(I) with length 48 = 72−1, defining interval I = {8,9,…,31}, and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(76, 11, F7, 5) (dual of [11, 5, 6]-code), using
- construction for [s, s−6, 6]-code from [s, 3, s−3]-code [i] based on linear OA(78, 11, F7, 7) (dual of [11, 3, 8]-code), using
- construction X applied to C1 ⊂ C0 [i] based on
- linear OA(77, 8, F7, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,7)), using code C1 for u = 2 by de Boer and Brouwer [i]
- linear OA(75, 8, F7, 5) (dual of [8, 3, 6]-code or 8-arc in PG(4,7)), using code C0 for u = 2 by de Boer and Brouwer [i]
- 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 C1 ⊂ C0 [i] based on
- construction for [s, s−6, 6]-code from [s, 3, s−3]-code [i] based on linear OA(78, 11, F7, 7) (dual of [11, 3, 8]-code), 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
None.