Information on Result #701003
Linear OA(428, 69, F4, 12) (dual of [69, 41, 13]-code), using construction XX applied to C1 = C({0,1,2,3,5,6,7,9,47}), C2 = C([0,10]), C3 = C1 + C2 = C([0,9]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,7,9,10,47}) based on
- linear OA(425, 63, F4, 11) (dual of [63, 38, 12]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,47}, and minimum distance d ≥ |{−1,0,…,9}|+1 = 12 (BCH-bound) [i]
- linear OA(425, 63, F4, 11) (dual of [63, 38, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(428, 63, F4, 12) (dual of [63, 35, 13]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,47}, and minimum distance d ≥ |{−1,0,…,10}|+1 = 13 (BCH-bound) [i]
- linear OA(422, 63, F4, 10) (dual of [63, 41, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- 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
- linear OA(40, 3, F4, 0) (dual of [3, 3, 1]-code) (see above)
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(428, 34, F4, 2, 12) (dual of [(34, 2), 40, 13]-NRT-code) | [i] | OOA Folding | |