Information on Result #712069
Linear OA(5143, 684, F5, 39) (dual of [684, 541, 40]-code), using construction XX applied to C1 = C([618,26]), C2 = C([0,32]), C3 = C1 + C2 = C([0,26]), and C∩ = C1 ∩ C2 = C([618,32]) based on
- linear OA(5103, 624, F5, 33) (dual of [624, 521, 34]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−6,−5,…,26}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(5103, 624, F5, 33) (dual of [624, 521, 34]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,32], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(5123, 624, F5, 39) (dual of [624, 501, 40]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−6,−5,…,32}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(583, 624, F5, 27) (dual of [624, 541, 28]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,26], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(510, 30, F5, 5) (dual of [30, 20, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(510, 52, F5, 5) (dual of [52, 42, 6]-code), using
- trace code [i] based on linear OA(255, 26, F25, 5) (dual of [26, 21, 6]-code or 26-arc in PG(4,25)), using
- extended Reed–Solomon code RSe(21,25) [i]
- the expurgated narrow-sense BCH-code C(I) with length 26 | 252−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- algebraic-geometric code AG(F,10P) with 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+6P) with degQ = 2 and degPÂ =Â 3 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
- trace code [i] based on linear OA(255, 26, F25, 5) (dual of [26, 21, 6]-code or 26-arc in PG(4,25)), using
- discarding factors / shortening the dual code based on linear OA(510, 52, F5, 5) (dual of [52, 42, 6]-code), using
- linear OA(510, 30, F5, 5) (dual of [30, 20, 6]-code) (see above)
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(5143, 342, F5, 2, 39) (dual of [(342, 2), 541, 40]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(5143, 228, F5, 3, 39) (dual of [(228, 3), 541, 40]-NRT-code) | [i] | ||