Information on Result #711815
Linear OA(5138, 687, F5, 37) (dual of [687, 549, 38]-code), using construction XX applied to C1 = C([136,166]), C2 = C([130,158]), C3 = C1 + C2 = C([136,158]), and C∩ = C1 ∩ C2 = C([130,166]) based on
- linear OA(597, 624, F5, 31) (dual of [624, 527, 32]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {136,137,…,166}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(591, 624, F5, 29) (dual of [624, 533, 30]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {130,131,…,158}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(5115, 624, F5, 37) (dual of [624, 509, 38]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {130,131,…,166}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(573, 624, F5, 23) (dual of [624, 551, 24]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {136,137,…,158}, and designed minimum distance d ≥ |I|+1 = 24 [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(59, 27, F5, 5) (dual of [27, 18, 6]-code), using
- construction X applied to C([0,2]) ⊂ C([1,2]) [i] based on
- linear OA(59, 26, F5, 5) (dual of [26, 17, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 26 | 54−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(58, 26, F5, 4) (dual of [26, 18, 5]-code), using the narrow-sense BCH-code C(I) with length 26 | 54−1, defining interval I = [1,2], and minimum distance d ≥ |{5,16,1}| + |{−9,−6,−3,0}∖{−3,−9}| = 5 (general Roos-bound) [i]
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to C([0,2]) ⊂ C([1,2]) [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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(5138, 343, F5, 2, 37) (dual of [(343, 2), 548, 38]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(5138, 229, F5, 3, 37) (dual of [(229, 3), 549, 38]-NRT-code) | [i] | ||