Information on Result #709995
Linear OA(578, 150, F5, 33) (dual of [150, 72, 34]-code), using construction XX applied to C1 = C([0,31]), C2 = C([10,32]), C3 = C1 + C2 = C([10,31]), and C∩ = C1 ∩ C2 = C([0,32]) based on
- linear OA(562, 124, F5, 32) (dual of [124, 62, 33]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [0,31], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(555, 124, F5, 23) (dual of [124, 69, 24]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {10,11,…,32}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(565, 124, F5, 33) (dual of [124, 59, 34]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [0,32], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(552, 124, F5, 22) (dual of [124, 72, 23]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {10,11,…,31}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(513, 23, F5, 9) (dual of [23, 10, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(513, 28, F5, 9) (dual of [28, 15, 10]-code), using
- 2 times truncation [i] based on linear OA(515, 30, F5, 11) (dual of [30, 15, 12]-code), using
- extended quadratic residue code Qe(30,5) [i]
- 2 times truncation [i] based on linear OA(515, 30, F5, 11) (dual of [30, 15, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(513, 28, F5, 9) (dual of [28, 15, 10]-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(578, 75, F5, 2, 33) (dual of [(75, 2), 72, 34]-NRT-code) | [i] | OOA Folding | |