Information on Result #1310347
Linear OA(531, 644, F5, 9) (dual of [644, 613, 10]-code), using 6 step Varšamov–Edel lengthening with (ri) = (1, 5 times 0) based on linear OA(530, 637, F5, 9) (dual of [637, 607, 10]-code), using
- construction XX applied to C1 = C([622,5]), C2 = C([0,6]), C3 = C1 + C2 = C([0,5]), and C∩ = C1 ∩ C2 = C([622,6]) [i] based on
- linear OA(525, 624, F5, 8) (dual of [624, 599, 9]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−2,−1,…,5}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(521, 624, F5, 7) (dual of [624, 603, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(529, 624, F5, 9) (dual of [624, 595, 10]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−2,−1,…,6}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(517, 624, F5, 6) (dual of [624, 607, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(51, 9, F5, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- 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
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(531, 644, F5, 2, 9) (dual of [(644, 2), 1257, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(531, 644, F5, 3, 9) (dual of [(644, 3), 1901, 10]-NRT-code) | [i] | ||
| 3 | Digital (22, 31, 644)-net over F5 | [i] | ||
| 4 | Linear OOA(531, 322, F5, 2, 9) (dual of [(322, 2), 613, 10]-NRT-code) | [i] | OOA Folding | |