Information on Result #712215
Linear OA(5122, 639, F5, 38) (dual of [639, 517, 39]-code), using construction XX applied to C1 = C([120,156]), C2 = C([123,157]), C3 = C1 + C2 = C([123,156]), and C∩ = C1 ∩ C2 = C([120,157]) 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 = {120,121,…,156}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(5111, 624, F5, 35) (dual of [624, 513, 36]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {123,124,…,157}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(5119, 624, F5, 38) (dual of [624, 505, 39]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {120,121,…,157}, and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(5107, 624, F5, 34) (dual of [624, 517, 35]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {123,124,…,156}, and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(53, 11, F5, 2) (dual of [11, 8, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), 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(5122, 213, F5, 3, 38) (dual of [(213, 3), 517, 39]-NRT-code) | [i] | OOA Folding | |