Information on Result #710786
Linear OA(5142, 327, F5, 47) (dual of [327, 185, 48]-code), using construction XX applied to C1 = C([33,78]), C2 = C([36,79]), C3 = C1 + C2 = C([36,78]), and C∩ = C1 ∩ C2 = C([33,79]) based on
- linear OA(5135, 312, F5, 46) (dual of [312, 177, 47]-code), using the BCH-code C(I) with length 312 | 54−1, defining interval I = {33,34,…,78}, and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(5131, 312, F5, 44) (dual of [312, 181, 45]-code), using the BCH-code C(I) with length 312 | 54−1, defining interval I = {36,37,…,79}, and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(5139, 312, F5, 47) (dual of [312, 173, 48]-code), using the BCH-code C(I) with length 312 | 54−1, defining interval I = {33,34,…,79}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(5127, 312, F5, 43) (dual of [312, 185, 44]-code), using the BCH-code C(I) with length 312 | 54−1, defining interval I = {36,37,…,78}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(53, 11, F5, 2) (dual of [11, 8, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- linear OA(50, 4, F5, 0) (dual of [4, 4, 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(5142, 163, F5, 2, 47) (dual of [(163, 2), 184, 48]-NRT-code) | [i] | OOA Folding | |