Information on Result #712397
Linear OA(5140, 637, F5, 44) (dual of [637, 497, 45]-code), using construction XX applied to C1 = C([622,40]), C2 = C([0,41]), C3 = C1 + C2 = C([0,40]), and C∩ = C1 ∩ C2 = C([622,41]) based on
- 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(5131, 624, F5, 42) (dual of [624, 493, 43]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,41], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(5139, 624, F5, 44) (dual of [624, 485, 45]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−2,−1,…,41}, and designed minimum distance d ≥ |I|+1 = 45 [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(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: 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(5140, 318, F5, 2, 44) (dual of [(318, 2), 496, 45]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(5140, 212, F5, 3, 44) (dual of [(212, 3), 496, 45]-NRT-code) | [i] | ||