Information on Result #711823
Linear OA(5124, 668, F5, 35) (dual of [668, 544, 36]-code), using construction XX applied to C1 = C([125,155]), C2 = C([131,159]), C3 = C1 + C2 = C([131,155]), and C∩ = C1 ∩ C2 = C([125,159]) based on
- linear OA(598, 624, F5, 31) (dual of [624, 526, 32]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {125,126,…,155}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(593, 624, F5, 29) (dual of [624, 531, 30]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {131,132,…,159}, and designed minimum distance d ≥ |I|+1 = 30 [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 = {125,126,…,159}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(580, 624, F5, 25) (dual of [624, 544, 26]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {131,132,…,155}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(59, 27, F5, 5) (dual of [27, 18, 6]-code), using
- construction X applied to C([0,2]) ⊂ C([1,2]) [i] based on
- linear OA(59, 26, F5, 5) (dual of [26, 17, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 26 | 54−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(58, 26, F5, 4) (dual of [26, 18, 5]-code), using the narrow-sense BCH-code C(I) with length 26 | 54−1, defining interval I = [1,2], and minimum distance d ≥ |{5,16,1}| + |{−9,−6,−3,0}∖{−3,−9}| = 5 (general Roos-bound) [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 C([0,2]) ⊂ C([1,2]) [i] based on
- linear OA(54, 17, F5, 3) (dual of [17, 13, 4]-code or 17-cap in PG(3,5)), 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(5124, 334, F5, 2, 35) (dual of [(334, 2), 544, 36]-NRT-code) | [i] | OOA Folding | |