Information on Result #712310
Linear OA(5125, 639, F5, 39) (dual of [639, 514, 40]-code), using construction XX applied to C1 = C([623,35]), C2 = C([1,37]), C3 = C1 + C2 = C([1,35]), and C∩ = C1 ∩ C2 = C([623,37]) based on
- linear OA(5115, 624, F5, 37) (dual of [624, 509, 38]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−1,0,…,35}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(5118, 624, F5, 37) (dual of [624, 506, 38]-code), using the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(5123, 624, F5, 39) (dual of [624, 501, 40]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−1,0,…,37}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(5110, 624, F5, 35) (dual of [624, 514, 36]-code), using the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(51, 6, F5, 1) (dual of [6, 5, 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(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 (see above)
Mode: Constructive and 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(5125, 319, F5, 2, 39) (dual of [(319, 2), 513, 40]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(5125, 213, F5, 3, 39) (dual of [(213, 3), 514, 40]-NRT-code) | [i] | ||