Information on Result #701087
Linear OA(461, 83, F4, 31) (dual of [83, 22, 32]-code), using construction XX applied to C1 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,31,43,47}), C2 = C([0,23]), C3 = C1 + C2 = C([0,22]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,31,43,47}) based on
- linear OA(450, 63, F4, 28) (dual of [63, 13, 29]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,31,43,47}, and minimum distance d ≥ |{−5,−4,…,22}|+1 = 29 (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(453, 63, F4, 31) (dual of [63, 10, 32]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,31,43,47}, and minimum distance d ≥ |{−5,−4,…,25}|+1 = 32 (BCH-bound) [i]
- linear OA(441, 63, F4, 23) (dual of [63, 22, 24]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(46, 15, F4, 4) (dual of [15, 9, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(46, 21, F4, 4) (dual of [21, 15, 5]-code), using
- linear OA(42, 5, F4, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,4)), using
- extended Reed–Solomon code RSe(3,4) [i]
- Hamming code H(2,4) [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(461, 41, F4, 2, 31) (dual of [(41, 2), 21, 32]-NRT-code) | [i] | OOA Folding | |