Information on Result #711361
Linear OA(5102, 666, F5, 28) (dual of [666, 564, 29]-code), using construction XX applied to C1 = C([130,155]), C2 = C([138,157]), C3 = C1 + C2 = C([138,155]), and C∩ = C1 ∩ C2 = C([130,157]) based on
- linear OA(582, 624, F5, 26) (dual of [624, 542, 27]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {130,131,…,155}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(565, 624, F5, 20) (dual of [624, 559, 21]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {138,139,…,157}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(587, 624, F5, 28) (dual of [624, 537, 29]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {130,131,…,157}, and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(560, 624, F5, 18) (dual of [624, 564, 19]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {138,139,…,155}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(514, 36, F5, 7) (dual of [36, 22, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(514, 52, F5, 7) (dual of [52, 38, 8]-code), using
- trace code [i] based on linear OA(257, 26, F25, 7) (dual of [26, 19, 8]-code or 26-arc in PG(6,25)), using
- extended Reed–Solomon code RSe(19,25) [i]
- the expurgated narrow-sense BCH-code C(I) with length 26 | 252−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- algebraic-geometric code AG(F,9P) 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,6P) with 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(257, 26, F25, 7) (dual of [26, 19, 8]-code or 26-arc in PG(6,25)), using
- discarding factors / shortening the dual code based on linear OA(514, 52, F5, 7) (dual of [52, 38, 8]-code), using
- linear OA(51, 6, F5, 1) (dual of [6, 5, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(5102, 222, F5, 3, 28) (dual of [(222, 3), 564, 29]-NRT-code) | [i] | OOA Folding | |