Information on Result #1310729
Linear OA(582, 640, F5, 25) (dual of [640, 558, 26]-code), using 7 step Varšamov–Edel lengthening with (ri) = (1, 6 times 0) based on linear OA(581, 632, F5, 25) (dual of [632, 551, 26]-code), using
- construction XX applied to C1 = C([623,22]), C2 = C([0,23]), C3 = C1 + C2 = C([0,22]), and C∩ = C1 ∩ C2 = C([623,23]) [i] based on
- linear OA(577, 624, F5, 24) (dual of [624, 547, 25]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−1,0,…,22}, and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(577, 624, F5, 24) (dual of [624, 547, 25]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,23], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(581, 624, F5, 25) (dual of [624, 543, 26]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−1,0,…,23}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(573, 624, F5, 23) (dual of [624, 551, 24]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(50, 4, F5, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(50, 4, F5, 0) (dual of [4, 4, 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(582, 640, F5, 2, 25) (dual of [(640, 2), 1198, 26]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(582, 640, F5, 3, 25) (dual of [(640, 3), 1838, 26]-NRT-code) | [i] | ||
| 3 | Digital (57, 82, 640)-net over F5 | [i] | ||
| 4 | Linear OOA(582, 320, F5, 2, 25) (dual of [(320, 2), 558, 26]-NRT-code) | [i] | OOA Folding | |