Information on Result #712258
Linear OA(5145, 670, F5, 42) (dual of [670, 525, 43]-code), using construction XX applied to C1 = C([618,31]), C2 = C([0,35]), C3 = C1 + C2 = C([0,31]), and C∩ = C1 ∩ C2 = C([618,35]) based on
- linear OA(5119, 624, F5, 38) (dual of [624, 505, 39]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−6,−5,…,31}, and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(5111, 624, F5, 36) (dual of [624, 513, 37]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,35], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(5131, 624, F5, 42) (dual of [624, 493, 43]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−6,−5,…,35}, and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(599, 624, F5, 32) (dual of [624, 525, 33]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,31], and designed minimum distance d ≥ |I|+1 = 33 [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(54, 16, F5, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,5)), 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(5145, 335, F5, 2, 42) (dual of [(335, 2), 525, 43]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(5145, 223, F5, 3, 42) (dual of [(223, 3), 524, 43]-NRT-code) | [i] | ||