Information on Result #710048
Linear OA(591, 155, F5, 40) (dual of [155, 64, 41]-code), using construction XX applied to C1 = C([117,30]), C2 = C([1,32]), C3 = C1 + C2 = C([1,30]), and C∩ = C1 ∩ C2 = C([117,32]) based on
- linear OA(576, 124, F5, 38) (dual of [124, 48, 39]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {−7,−6,…,30}, and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(564, 124, F5, 32) (dual of [124, 60, 33]-code), using the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(580, 124, F5, 40) (dual of [124, 44, 41]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {−7,−6,…,32}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(560, 124, F5, 30) (dual of [124, 64, 31]-code), using the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(510, 26, F5, 7) (dual of [26, 16, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(510, 25, F5, 7) (dual of [25, 15, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(59, 25, F5, 6) (dual of [25, 16, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(50, 1, F5, 0) (dual of [1, 1, 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
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- 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 OA(591, 155, F5, 39) (dual of [155, 64, 40]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(589, 153, F5, 38) (dual of [153, 64, 39]-code) | [i] | Truncation | |
| 3 | Linear OOA(591, 77, F5, 2, 40) (dual of [(77, 2), 63, 41]-NRT-code) | [i] | OOA Folding | |