Information on Result #685934
Linear OA(749, 57, F7, 38) (dual of [57, 8, 39]-code), using construction XX applied to C1 = C([0,65]), C2 = C([1,79]), C3 = C1 + C2 = C([1,65]), and C∩ = C1 ∩ C2 = C([0,79]) based on
- linear OA(741, 48, F7, 33) (dual of [48, 7, 34]-code), using contraction [i] based on linear OA(789, 96, F7, 67) (dual of [96, 7, 68]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [0,65], and minimum distance d ≥ |{−1,0,…,65}|+1 = 68 (BCH-bound) [i]
- linear OA(744, 48, F7, 39) (dual of [48, 4, 40]-code), using contraction [i] based on linear OA(792, 96, F7, 79) (dual of [96, 4, 80]-code), using the narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [1,79], and designed minimum distance d ≥ |I|+1 = 80 [i]
- linear OA(745, 48, F7, 40) (dual of [48, 3, 41]-code), using contraction [i] based on linear OA(793, 96, F7, 81) (dual of [96, 3, 82]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [0,79], and minimum distance d ≥ |{−1,0,…,79}|+1 = 82 (BCH-bound) [i]
- linear OA(740, 48, F7, 32) (dual of [48, 8, 33]-code), using contraction [i] based on linear OA(788, 96, F7, 65) (dual of [96, 8, 66]-code), using the narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [1,65], and designed minimum distance d ≥ |I|+1 = 66 [i]
- linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- 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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(747, 55, F7, 36) (dual of [55, 8, 37]-code) | [i] | Truncation | |
| 2 | Linear OOA(749, 28, F7, 2, 38) (dual of [(28, 2), 7, 39]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(749, 19, F7, 3, 38) (dual of [(19, 3), 8, 39]-NRT-code) | [i] | ||