Information on Result #685901
Linear OA(769, 78, F7, 47) (dual of [78, 9, 48]-code), using construction XX applied to C([1,95]) ⊂ C([1,65]) ⊂ C([1,63]) based on
- linear OA(747, 48, F7, 47) (dual of [48, 1, 48]-code or 48-arc in PG(46,7)), using contraction [i] based on linear OA(795, 96, F7, 95) (dual of [96, 1, 96]-code or 96-arc in PG(94,7)), using the narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [1,95], and designed minimum distance d ≥ |I|+1 = 96 [i]
- linear OA(740, 48, F7, 32) (dual of [48, 8, 33]-code), using contraction [i] based on linear OA(788, 96, F7, 65) (dual of [96, 8, 66]-code), using the narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [1,65], and designed minimum distance d ≥ |I|+1 = 66 [i]
- linear OA(739, 48, F7, 31) (dual of [48, 9, 32]-code), using contraction [i] based on linear OA(787, 96, F7, 63) (dual of [96, 9, 64]-code), using the narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [1,63], and designed minimum distance d ≥ |I|+1 = 64 [i]
- linear OA(721, 29, F7, 14) (dual of [29, 8, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(721, 30, F7, 14) (dual of [30, 9, 15]-code), using
- generalized (u, u+v)-construction [i] based on
- linear OA(72, 5, F7, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,7)), using
- discarding factors / shortening the dual code based on linear OA(72, 7, F7, 2) (dual of [7, 5, 3]-code or 7-arc in PG(1,7)), using
- Reed–Solomon code RS(5,7) [i]
- discarding factors / shortening the dual code based on linear OA(72, 7, F7, 2) (dual of [7, 5, 3]-code or 7-arc in PG(1,7)), using
- linear OA(72, 5, F7, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,7)) (see above)
- linear OA(73, 5, F7, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,7) or 5-cap in PG(2,7)), using
- discarding factors / shortening the dual code based on linear OA(73, 7, F7, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,7) or 7-cap in PG(2,7)), using
- Reed–Solomon code RS(4,7) [i]
- discarding factors / shortening the dual code based on linear OA(73, 7, F7, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,7) or 7-cap in PG(2,7)), using
- linear OA(74, 5, F7, 4) (dual of [5, 1, 5]-code or 5-arc in PG(3,7)), using
- dual of repetition code with length 5 [i]
- linear OA(75, 5, F7, 5) (dual of [5, 0, 6]-code or 5-arc in PG(4,7)), using
- linear OA(75, 5, F7, 5) (dual of [5, 0, 6]-code or 5-arc in PG(4,7)) (see above)
- linear OA(72, 5, F7, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,7)), using
- generalized (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(721, 30, F7, 14) (dual of [30, 9, 15]-code), using
- linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [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.