Information on Result #677602
Linear OA(383, 89, F3, 54) (dual of [89, 6, 55]-code), using construction XX applied to C([1,159]) ⊂ C([1,105]) ⊂ C([1,99]) based on
- linear OA(379, 80, F3, 79) (dual of [80, 1, 80]-code or 80-arc in PG(78,3)), using contraction [i] based on linear OA(3159, 160, F3, 159) (dual of [160, 1, 160]-code or 160-arc in PG(158,3)), using the narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [1,159], and designed minimum distance d ≥ |I|+1 = 160 [i]
- linear OA(375, 80, F3, 52) (dual of [80, 5, 53]-code), using contraction [i] based on linear OA(3155, 160, F3, 105) (dual of [160, 5, 106]-code), using the narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [1,105], and designed minimum distance d ≥ |I|+1 = 106 [i]
- linear OA(373, 80, F3, 49) (dual of [80, 7, 50]-code), using contraction [i] based on linear OA(3153, 160, F3, 99) (dual of [160, 7, 100]-code), using the narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [1,99], and designed minimum distance d ≥ |I|+1 = 100 [i]
- linear OA(31, 6, F3, 1) (dual of [6, 5, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(32, 3, F3, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,3)), using
- dual of repetition code with length 3 [i]
- Reed–Solomon code RS(1,3) [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
None.