Information on Result #685784
Linear OA(753, 127, F7, 22) (dual of [127, 74, 23]-code), using construction XX applied to Ce(21) ⊂ Ce(18) ⊂ Ce(15) based on
- linear OA(747, 115, F7, 22) (dual of [115, 68, 23]-code), using an extension Ce(21) of the narrow-sense BCH-code C(I) with length 114 | 73−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(743, 115, F7, 19) (dual of [115, 72, 20]-code), using an extension Ce(18) of the narrow-sense BCH-code C(I) with length 114 | 73−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(740, 115, F7, 16) (dual of [115, 75, 17]-code), using an extension Ce(15) of the narrow-sense BCH-code C(I) with length 114 | 73−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(72, 4, F7, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,7)), using
- discarding factors / shortening the dual code based on linear OA(72, 7, F7, 2) (dual of [7, 5, 3]-code or 7-arc in PG(1,7)), using
- Reed–Solomon code RS(5,7) [i]
- discarding factors / shortening the dual code based on linear OA(72, 7, F7, 2) (dual of [7, 5, 3]-code or 7-arc in PG(1,7)), 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.
Other Results with Identical Parameters
None.
Depending Results
None.