Information on Result #709910
Linear OA(543, 136, F5, 17) (dual of [136, 93, 18]-code), using construction XX applied to C1 = C([16,31]), C2 = C([19,32]), C3 = C1 + C2 = C([19,31]), and C∩ = C1 ∩ C2 = C([16,32]) based on
- linear OA(537, 124, F5, 16) (dual of [124, 87, 17]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {16,17,…,31}, and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(534, 124, F5, 14) (dual of [124, 90, 15]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {19,20,…,32}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(540, 124, F5, 17) (dual of [124, 84, 18]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {16,17,…,32}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(531, 124, F5, 13) (dual of [124, 93, 14]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {19,20,…,31}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(53, 9, F5, 2) (dual of [9, 6, 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, 3, F5, 0) (dual of [3, 3, 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(543, 68, F5, 2, 17) (dual of [(68, 2), 93, 18]-NRT-code) | [i] | OOA Folding | |