Information on Result #712387
Linear OA(5137, 638, F5, 43) (dual of [638, 501, 44]-code), using construction XX applied to C1 = C([622,38]), C2 = C([0,40]), C3 = C1 + C2 = C([0,38]), and C∩ = C1 ∩ C2 = C([622,40]) based on
- linear OA(5131, 624, F5, 41) (dual of [624, 493, 42]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−2,−1,…,38}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(5127, 624, F5, 41) (dual of [624, 497, 42]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,40], and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(5135, 624, F5, 43) (dual of [624, 489, 44]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−2,−1,…,40}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(5123, 624, F5, 39) (dual of [624, 501, 40]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,38], and designed minimum distance d ≥ |I|+1 = 40 [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(51, 5, F5, 1) (dual of [5, 4, 2]-code), using
- Reed–Solomon code RS(4,5) [i]
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(5137, 319, F5, 2, 43) (dual of [(319, 2), 501, 44]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(5137, 212, F5, 3, 43) (dual of [(212, 3), 499, 44]-NRT-code) | [i] | ||