Information on Result #701084
Linear OA(454, 76, F4, 28) (dual of [76, 22, 29]-code), using construction XX applied to C1 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,31,47}), C2 = C([0,23]), C3 = C1 + C2 = C([0,21]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,31,47}) based on
- linear OA(444, 63, F4, 26) (dual of [63, 19, 27]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,31,47}, and minimum distance d ≥ |{−4,−3,…,21}|+1 = 27 (BCH-bound) [i]
- linear OA(444, 63, F4, 26) (dual of [63, 19, 27]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,23], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(450, 63, F4, 30) (dual of [63, 13, 31]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,31,47}, and minimum distance d ≥ |{−4,−3,…,25}|+1 = 31 (BCH-bound) [i]
- linear OA(438, 63, F4, 22) (dual of [63, 25, 23]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(43, 6, F4, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,4) or 6-cap in PG(2,4)), using
- 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
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(454, 38, F4, 2, 28) (dual of [(38, 2), 22, 29]-NRT-code) | [i] | OOA Folding | |