Information on Result #724705
Linear OA(25102, 670, F25, 46) (dual of [670, 568, 47]-code), using construction XX applied to C1 = C([615,29]), C2 = C([0,36]), C3 = C1 + C2 = C([0,29]), and C∩ = C1 ∩ C2 = C([615,36]) based on
- linear OA(2574, 624, F25, 39) (dual of [624, 550, 40]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−9,−8,…,29}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(2570, 624, F25, 37) (dual of [624, 554, 38]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,36], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(2588, 624, F25, 46) (dual of [624, 536, 47]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−9,−8,…,36}, and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(2556, 624, F25, 30) (dual of [624, 568, 31]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,29], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(258, 26, F25, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,25)), using
- extended Reed–Solomon code RSe(18,25) [i]
- algebraic-geometric code AG(F, Q+7P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using the rational function field F25(x) [i]
- algebraic-geometric code AG(F, Q+5P) with degQ = 2 and degPÂ =Â 3 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
- linear OA(256, 20, F25, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,25)), using
- discarding factors / shortening the dual code based on linear OA(256, 25, F25, 6) (dual of [25, 19, 7]-code or 25-arc in PG(5,25)), using
- Reed–Solomon code RS(19,25) [i]
- discarding factors / shortening the dual code based on linear OA(256, 25, F25, 6) (dual of [25, 19, 7]-code or 25-arc in PG(5,25)), 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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(25102, 335, F25, 2, 46) (dual of [(335, 2), 568, 47]-NRT-code) | [i] | OOA Folding | |