Information on Result #1314383
Linear OA(2539, 1162, F25, 16) (dual of [1162, 1123, 17]-code), using 526 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 0, 1, 13 times 0, 1, 39 times 0, 1, 91 times 0, 1, 157 times 0, 1, 217 times 0) based on 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]) [i] 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: 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(2539, 1162, F25, 2, 16) (dual of [(1162, 2), 2285, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (23, 39, 1162)-net over F25 | [i] | ||
| 3 | Linear OOA(2539, 581, F25, 2, 16) (dual of [(581, 2), 1123, 17]-NRT-code) | [i] | OOA Folding | |