Information on Result #685946
Linear OA(745, 60, F7, 30) (dual of [60, 15, 31]-code), using construction XX applied to C1 = C([0,49]), C2 = C([1,63]), C3 = C1 + C2 = C([1,49]), and C∩ = C1 ∩ C2 = C([0,63]) based on
- linear OA(734, 48, F7, 25) (dual of [48, 14, 26]-code), using contraction [i] based on linear OA(782, 96, F7, 51) (dual of [96, 14, 52]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [0,49], and minimum distance d ≥ |{−1,0,…,49}|+1 = 52 (BCH-bound) [i]
- linear OA(739, 48, F7, 31) (dual of [48, 9, 32]-code), using contraction [i] based on linear OA(787, 96, F7, 63) (dual of [96, 9, 64]-code), using the narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [1,63], and designed minimum distance d ≥ |I|+1 = 64 [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 expurgated narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [0,63], and minimum distance d ≥ |{−1,0,…,63}|+1 = 66 (BCH-bound) [i]
- linear OA(733, 48, F7, 24) (dual of [48, 15, 25]-code), using contraction [i] based on linear OA(781, 96, F7, 49) (dual of [96, 15, 50]-code), using the narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [1,49], and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- 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, using the rational function field F7(x) [i]
- 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
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(749, 68, F7, 30) (dual of [68, 19, 31]-code) | [i] | Varšamov–Edel Lengthening | |
| 2 | Linear OOA(745, 30, F7, 2, 30) (dual of [(30, 2), 15, 31]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(745, 20, F7, 3, 30) (dual of [(20, 3), 15, 31]-NRT-code) | [i] | ||