Information on Result #723425
Linear OA(2531, 628, F25, 16) (dual of [628, 597, 17]-code), using construction XX applied to C1 = C([623,13]), C2 = C([0,14]), C3 = C1 + C2 = C([0,13]), and C∩ = C1 ∩ C2 = C([623,14]) based on
- linear OA(2529, 624, F25, 15) (dual of [624, 595, 16]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,13}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(2529, 624, F25, 15) (dual of [624, 595, 16]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(2531, 624, F25, 16) (dual of [624, 593, 17]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,14}, and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2527, 624, F25, 14) (dual of [624, 597, 15]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- 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
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code) (see above)
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 OA(2539, 654, F25, 16) (dual of [654, 615, 17]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(2540, 657, F25, 16) (dual of [657, 617, 17]-code) | [i] | ||
| 3 | Linear OA(2541, 659, F25, 16) (dual of [659, 618, 17]-code) | [i] | ||
| 4 | Linear OA(2542, 680, F25, 16) (dual of [680, 638, 17]-code) | [i] | ||
| 5 | Linear OA(2543, 694, F25, 16) (dual of [694, 651, 17]-code) | [i] | ||
| 6 | Linear OA(2544, 708, F25, 16) (dual of [708, 664, 17]-code) | [i] | ||
| 7 | Linear OA(2535, 650, F25, 16) (dual of [650, 615, 17]-code) | [i] | Varšamov–Edel Lengthening | |
| 8 | Linear OA(2536, 691, F25, 16) (dual of [691, 655, 17]-code) | [i] | ||
| 9 | Linear OA(2537, 784, F25, 16) (dual of [784, 747, 17]-code) | [i] | ||
| 10 | Linear OA(2538, 943, F25, 16) (dual of [943, 905, 17]-code) | [i] | ||
| 11 | Linear OA(2539, 1162, F25, 16) (dual of [1162, 1123, 17]-code) | [i] | ||
| 12 | Linear OOA(2531, 314, F25, 2, 16) (dual of [(314, 2), 597, 17]-NRT-code) | [i] | OOA Folding | |