Information on Result #701252
Linear OA(549, 80, F5, 22) (dual of [80, 31, 23]-code), using construction XX applied to C1 = C({0,1,2,3,4,6,7,8,9,11,12,24,37,47}), C2 = C([0,16]), C3 = C1 + C2 = C([0,12]), and C∩ = C1 ∩ C2 = C({0,1,2,3,4,6,7,8,9,11,12,16,24,37,47}) based on
- linear OA(540, 62, F5, 21) (dual of [62, 22, 22]-code), using the cyclic code C(A) with length 62 | 53−1, defining set A = {0,1,2,3,4,6,7,8,9,11,12,24,37,47}, and minimum distance d ≥ |{−5,−4,…,15}|+1 = 22 (BCH-bound) [i]
- linear OA(534, 62, F5, 17) (dual of [62, 28, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 62 | 53−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(543, 62, F5, 22) (dual of [62, 19, 23]-code), using the cyclic code C(A) with length 62 | 53−1, defining set A = {0,1,2,3,4,6,7,8,9,11,12,16,24,37,47}, and minimum distance d ≥ |{−5,−4,…,16}|+1 = 23 (BCH-bound) [i]
- linear OA(531, 62, F5, 16) (dual of [62, 31, 17]-code), using the expurgated narrow-sense BCH-code C(I) with length 62 | 53−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(56, 15, F5, 4) (dual of [15, 9, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(56, 30, F5, 4) (dual of [30, 24, 5]-code), using
- linear OA(50, 3, F5, 0) (dual of [3, 3, 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.
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Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(549, 40, F5, 2, 22) (dual of [(40, 2), 31, 23]-NRT-code) | [i] | OOA Folding | |