Information on Result #732758
Linear OA(2555, 700, F25, 20) (dual of [700, 645, 21]-code), using (u, u+v)-construction based on
- linear OA(2514, 66, F25, 10) (dual of [66, 52, 11]-code), using
- extended algebraic-geometric code AGe(F,55P) [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- linear OA(2541, 634, F25, 20) (dual of [634, 593, 21]-code), using
- construction XX applied to C1 = C([621,15]), C2 = C([0,16]), C3 = C1 + C2 = C([0,15]), and C∩ = C1 ∩ C2 = C([621,16]) [i] based on
- linear OA(2537, 624, F25, 19) (dual of [624, 587, 20]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−3,−2,…,15}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(2533, 624, F25, 17) (dual of [624, 591, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(2539, 624, F25, 20) (dual of [624, 585, 21]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−3,−2,…,16}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(2531, 624, F25, 16) (dual of [624, 593, 17]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(252, 8, F25, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,25)), using
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- Reed–Solomon code RS(23,25) [i]
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction XX applied to C1 = C([621,15]), C2 = C([0,16]), C3 = C1 + C2 = C([0,15]), and C∩ = C1 ∩ C2 = C([621,16]) [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(2555, 350, F25, 2, 20) (dual of [(350, 2), 645, 21]-NRT-code) | [i] | OOA Folding | |