Information on Result #701013
Linear OA(455, 93, F4, 23) (dual of [93, 38, 24]-code), using construction XX applied to C1 = C({0,1,2,3,5,6,7,9,10,14,22,26,30,42}), C2 = C([0,11]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,7,9,10,11,14,22,26,30,42}) based on
- linear OA(438, 63, F4, 22) (dual of [63, 25, 23]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,14,22,26,30,42}, and minimum distance d ≥ |{0,2,4,…,42}|+1 = 23 (BCH-bound) [i]
- linear OA(428, 63, F4, 13) (dual of [63, 35, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(441, 63, F4, 23) (dual of [63, 22, 24]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,14,22,26,30,42}, and minimum distance d ≥ |{0,2,4,…,44}|+1 = 24 (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(413, 26, F4, 9) (dual of [26, 13, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(413, 28, F4, 9) (dual of [28, 15, 10]-code), using
- 2 times truncation [i] based on linear OA(415, 30, F4, 11) (dual of [30, 15, 12]-code), using
- extended quadratic residue code Qe(30,4) [i]
- 2 times truncation [i] based on linear OA(415, 30, F4, 11) (dual of [30, 15, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(413, 28, F4, 9) (dual of [28, 15, 10]-code), using
- linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), using
- Reed–Solomon code RS(3,4) [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(455, 46, F4, 2, 23) (dual of [(46, 2), 37, 24]-NRT-code) | [i] | OOA Folding | |