Information on Result #701167
Linear OA(514, 31, F5, 8) (dual of [31, 17, 9]-code), using construction XX applied to C1 = C({1,3,4,6,7}), C2 = C([0,6]), C3 = C1 + C2 = C({1,3,4,6}), and C∩ = C1 ∩ C2 = C([0,7]) based on
- linear OA(59, 24, F5, 5) (dual of [24, 15, 6]-code), using the primitive cyclic code C(A) with length 24 = 52−1, defining set A = {1,3,4,6,7}, and minimum distance d ≥ |{3,4,5,6,7}|+1 = 6 (BCH-bound) [i]
- linear OA(510, 24, F5, 7) (dual of [24, 14, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(512, 24, F5, 8) (dual of [24, 12, 9]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(57, 24, F5, 4) (dual of [24, 17, 5]-code), using the primitive cyclic code C(A) with length 24 = 52−1, defining set A = {1,3,4,6}, and minimum distance d ≥ |{3,4,5,6}|+1 = 5 (BCH-bound) [i]
- linear OA(50, 2, F5, 0) (dual of [2, 2, 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
- linear OA(52, 5, F5, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,5)), using
- Reed–Solomon code RS(3,5) [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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(514, 15, F5, 2, 8) (dual of [(15, 2), 16, 9]-NRT-code) | [i] | OOA Folding | |