Information on Result #700979
Linear OA(420, 73, F4, 8) (dual of [73, 53, 9]-code), using construction XX applied to C1 = C({0,1,2,3,31,47}), C2 = C([0,5]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,31,47}) based on
- linear OA(416, 63, F4, 7) (dual of [63, 47, 8]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,31,47}, and minimum distance d ≥ |{−2,−1,…,4}|+1 = 8 (BCH-bound) [i]
- linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(419, 63, F4, 8) (dual of [63, 44, 9]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,31,47}, and minimum distance d ≥ |{−2,−1,…,5}|+1 = 9 (BCH-bound) [i]
- linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(41, 7, F4, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(40, 3, F4, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 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.
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 OA(4253, 65609, F4, 39) (dual of [65609, 65356, 40]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 2 | Linear OA(4245, 65609, F4, 38) (dual of [65609, 65364, 39]-code) | [i] | ||
| 3 | Linear OA(4237, 65609, F4, 36) (dual of [65609, 65372, 37]-code) | [i] | ||
| 4 | Linear OA(4229, 65609, F4, 35) (dual of [65609, 65380, 36]-code) | [i] | ||
| 5 | Linear OA(4221, 65609, F4, 34) (dual of [65609, 65388, 35]-code) | [i] | ||
| 6 | Linear OA(4213, 65609, F4, 32) (dual of [65609, 65396, 33]-code) | [i] | ||
| 7 | Linear OA(4205, 65609, F4, 31) (dual of [65609, 65404, 32]-code) | [i] | ||
| 8 | Linear OA(4197, 65609, F4, 30) (dual of [65609, 65412, 31]-code) | [i] | ||
| 9 | Linear OOA(420, 36, F4, 2, 8) (dual of [(36, 2), 52, 9]-NRT-code) | [i] | OOA Folding | |