Information on Result #1314422
Linear OA(2549, 702, F25, 22) (dual of [702, 653, 23]-code), using 68 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 5 times 0, 1, 16 times 0, 1, 42 times 0) based on linear OA(2543, 628, F25, 22) (dual of [628, 585, 23]-code), using
- construction XX applied to C1 = C([623,19]), C2 = C([0,20]), C3 = C1 + C2 = C([0,19]), and C∩ = C1 ∩ C2 = C([623,20]) [i] based on
- linear OA(2541, 624, F25, 21) (dual of [624, 583, 22]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,19}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2541, 624, F25, 21) (dual of [624, 583, 22]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2543, 624, F25, 22) (dual of [624, 581, 23]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,20}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2539, 624, F25, 20) (dual of [624, 585, 21]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [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(2549, 702, F25, 2, 22) (dual of [(702, 2), 1355, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (27, 49, 702)-net over F25 | [i] | ||
| 3 | Linear OOA(2549, 351, F25, 2, 22) (dual of [(351, 2), 653, 23]-NRT-code) | [i] | OOA Folding | |