Information on Result #701268
Linear OA(544, 75, F5, 21) (dual of [75, 31, 22]-code), using construction XX applied to C1 = C({0,1,2,3,4,6,7,8,9,11,12,37}), C2 = C([0,17]), C3 = C1 + C2 = C([0,12]), and C∩ = C1 ∩ C2 = C({0,1,2,3,4,6,7,8,9,11,12,16,17,37}) based on
- linear OA(534, 62, F5, 18) (dual of [62, 28, 19]-code), using the cyclic code C(A) with length 62 | 53−1, defining set A = {0,1,2,3,4,6,7,8,9,11,12,37}, and minimum distance d ≥ |{−2,−1,…,15}|+1 = 19 (BCH-bound) [i]
- linear OA(537, 62, F5, 19) (dual of [62, 25, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 62 | 53−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 20 [i]
- 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 = {0,1,2,3,4,6,7,8,9,11,12,16,17,37}, and minimum distance d ≥ |{−2,−1,…,18}|+1 = 22 (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(51, 4, F5, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, 5, F5, 1) (dual of [5, 4, 2]-code), using
- Reed–Solomon code RS(4,5) [i]
- discarding factors / shortening the dual code based on linear OA(51, 5, F5, 1) (dual of [5, 4, 2]-code), using
- linear OA(53, 9, F5, 2) (dual of [9, 6, 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
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(544, 37, F5, 2, 21) (dual of [(37, 2), 30, 22]-NRT-code) | [i] | OOA Folding | |