Information on Result #1310944
Linear OA(5106, 679, F5, 33) (dual of [679, 573, 34]-code), using 44 step Varšamov–Edel lengthening with (ri) = (1, 0, 0, 0, 1, 13 times 0, 1, 25 times 0) based on linear OA(5103, 632, F5, 33) (dual of [632, 529, 34]-code), using
- construction XX applied to C1 = C([623,30]), C2 = C([0,31]), C3 = C1 + C2 = C([0,30]), and C∩ = C1 ∩ C2 = C([623,31]) [i] based on
- linear OA(599, 624, F5, 32) (dual of [624, 525, 33]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−1,0,…,30}, and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(599, 624, F5, 32) (dual of [624, 525, 33]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,31], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(5103, 624, F5, 33) (dual of [624, 521, 34]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−1,0,…,31}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(595, 624, F5, 31) (dual of [624, 529, 32]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,30], and designed minimum distance d ≥ |I|+1 = 32 [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(5106, 679, F5, 2, 33) (dual of [(679, 2), 1252, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5106, 679, F5, 3, 33) (dual of [(679, 3), 1931, 34]-NRT-code) | [i] | ||
| 3 | Digital (73, 106, 679)-net over F5 | [i] | ||
| 4 | Linear OOA(5106, 339, F5, 2, 33) (dual of [(339, 2), 572, 34]-NRT-code) | [i] | OOA Folding | |