Information on Result #681935
Linear OA(455, 81, F4, 27) (dual of [81, 26, 28]-code), using construction X applied to C([0,80]) ⊂ C([0,62]) based on
- linear OA(447, 63, F4, 27) (dual of [63, 16, 28]-code), using contraction [i] based on linear OA(4173, 189, F4, 83) (dual of [189, 16, 84]-code), using the expurgated narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [0,80], and minimum distance d ≥ |{−2,−1,…,80}|+1 = 84 (BCH-bound) [i]
- linear OA(437, 63, F4, 21) (dual of [63, 26, 22]-code), using contraction [i] based on linear OA(4163, 189, F4, 65) (dual of [189, 26, 66]-code), using the expurgated narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [0,62], and minimum distance d ≥ |{−2,−1,…,62}|+1 = 66 (BCH-bound) [i]
- linear OA(48, 18, F4, 5) (dual of [18, 10, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(48, 19, F4, 5) (dual of [19, 11, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(2) [i] based on
- linear OA(47, 16, F4, 5) (dual of [16, 9, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 15 = 42−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(45, 16, F4, 3) (dual of [16, 11, 4]-code or 16-cap in PG(4,4)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 15 = 42−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(41, 3, F4, 1) (dual of [3, 2, 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
- construction X applied to Ce(4) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(48, 19, F4, 5) (dual of [19, 11, 6]-code), 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
None.