Information on Result #685905
Linear OA(751, 60, F7, 38) (dual of [60, 9, 39]-code), using construction XX applied to C([1,79]) ⊂ C([1,65]) ⊂ C([1,63]) based on
- linear OA(744, 48, F7, 39) (dual of [48, 4, 40]-code), using contraction [i] based on linear OA(792, 96, F7, 79) (dual of [96, 4, 80]-code), using the narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [1,79], and designed minimum distance d ≥ |I|+1 = 80 [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(76, 11, F7, 5) (dual of [11, 5, 6]-code), using
- construction for [s, s−6, 6]-code from [s, 3, s−3]-code [i] based on linear OA(78, 11, F7, 7) (dual of [11, 3, 8]-code), using
- construction X applied to C1 ⊂ C0 [i] based on
- linear OA(77, 8, F7, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,7)), using code C1 for u = 2 by de Boer and Brouwer [i]
- linear OA(75, 8, F7, 5) (dual of [8, 3, 6]-code or 8-arc in PG(4,7)), using code C0 for u = 2 by de Boer and Brouwer [i]
- linear OA(71, 3, F7, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C1 ⊂ C0 [i] based on
- construction for [s, s−6, 6]-code from [s, 3, s−3]-code [i] based on linear OA(78, 11, F7, 7) (dual of [11, 3, 8]-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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(751, 60, F7, 37) (dual of [60, 9, 38]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(751, 60, F7, 36) (dual of [60, 9, 37]-code) | [i] | ||
| 3 | Linear OOA(751, 30, F7, 2, 38) (dual of [(30, 2), 9, 39]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(751, 20, F7, 3, 38) (dual of [(20, 3), 9, 39]-NRT-code) | [i] | ||