Information on Result #711907
Linear OA(5134, 679, F5, 37) (dual of [679, 545, 38]-code), using construction XX applied to C1 = C([136,166]), C2 = C([130,159]), C3 = C1 + C2 = C([136,159]), and C∩ = C1 ∩ C2 = C([130,166]) based on
- linear OA(597, 624, F5, 31) (dual of [624, 527, 32]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {136,137,…,166}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(595, 624, F5, 30) (dual of [624, 529, 31]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {130,131,…,159}, and designed minimum distance d ≥ |I|+1 = 31 [i]
- 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 = {130,131,…,166}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(577, 624, F5, 24) (dual of [624, 547, 25]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {136,137,…,159}, and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(510, 28, F5, 6) (dual of [28, 18, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(3) [i] based on
- 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(57, 25, F5, 4) (dual of [25, 18, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(51, 3, F5, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(3) [i] based on
- 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
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(5134, 339, F5, 2, 37) (dual of [(339, 2), 544, 38]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(5134, 226, F5, 3, 37) (dual of [(226, 3), 544, 38]-NRT-code) | [i] | ||