Information on Result #732416
Linear OA(2586, 706, F25, 33) (dual of [706, 620, 34]-code), using (u, u+v)-construction based on
- linear OA(2520, 66, F25, 16) (dual of [66, 46, 17]-code), using
- extended algebraic-geometric code AGe(F,49P) [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- linear OA(2566, 640, F25, 33) (dual of [640, 574, 34]-code), using
- construction XX applied to C1 = C([619,26]), C2 = C([0,27]), C3 = C1 + C2 = C([0,26]), and C∩ = C1 ∩ C2 = C([619,27]) [i] based on
- linear OA(2560, 624, F25, 32) (dual of [624, 564, 33]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−5,−4,…,26}, and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(2552, 624, F25, 28) (dual of [624, 572, 29]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,27], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2562, 624, F25, 33) (dual of [624, 562, 34]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−5,−4,…,27}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(2550, 624, F25, 27) (dual of [624, 574, 28]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,26], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(254, 14, F25, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,25)), using
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
- Reed–Solomon code RS(21,25) [i]
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), 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([619,26]), C2 = C([0,27]), C3 = C1 + C2 = C([0,26]), and C∩ = C1 ∩ C2 = C([619,27]) [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(2586, 353, F25, 2, 33) (dual of [(353, 2), 620, 34]-NRT-code) | [i] | OOA Folding | |