Information on Result #712009
Linear OA(5141, 678, F5, 39) (dual of [678, 537, 40]-code), using construction XX applied to C1 = C([617,26]), C2 = C([0,31]), C3 = C1 + C2 = C([0,26]), and C∩ = C1 ∩ C2 = C([617,31]) based on
- linear OA(5107, 624, F5, 34) (dual of [624, 517, 35]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−7,−6,…,26}, and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(599, 624, F5, 32) (dual of [624, 525, 33]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,31], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(5123, 624, F5, 39) (dual of [624, 501, 40]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−7,−6,…,31}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(583, 624, F5, 27) (dual of [624, 541, 28]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,26], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(511, 31, F5, 6) (dual of [31, 20, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(2) [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(55, 25, F5, 3) (dual of [25, 20, 4]-code or 25-cap in PG(4,5)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(52, 6, F5, 2) (dual of [6, 4, 3]-code or 6-arc in PG(1,5)), using
- extended Reed–Solomon code RSe(4,5) [i]
- Hamming code H(2,5) [i]
- construction X applied to Ce(5) ⊂ Ce(2) [i] based on
- linear OA(57, 23, F5, 4) (dual of [23, 16, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(57, 24, F5, 4) (dual of [24, 17, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(57, 24, F5, 4) (dual of [24, 17, 5]-code), 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(5141, 339, F5, 2, 39) (dual of [(339, 2), 537, 40]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(5141, 226, F5, 3, 39) (dual of [(226, 3), 537, 40]-NRT-code) | [i] | ||