Information on Result #685921

Linear OA(757, 66, F7, 41) (dual of [66, 9, 42]-code), using construction XX applied to C([0,81]) ⊂ C([0,63]) ⊂ C([1,63]) based on
  1. linear OA(746, 48, F7, 41) (dual of [48, 2, 42]-code), using contraction [i] based on linear OA(794, 96, F7, 83) (dual of [96, 2, 84]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [0,81], and minimum distance d ≥ |{15,32,49,…,−31}|+1 = 84 (BCH-bound) [i]
  2. 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 expurgated narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [0,63], and minimum distance d ≥ |{−1,0,…,63}|+1 = 66 (BCH-bound) [i]
  3. 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]
  4. linear OA(710, 17, F7, 8) (dual of [17, 7, 9]-code), using
  5. linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-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

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(757, 66, F7, 40) (dual of [66, 9, 41]-code) [i]Strength Reduction
2Linear OOA(757, 33, F7, 2, 41) (dual of [(33, 2), 9, 42]-NRT-code) [i]OOA Folding
3Linear OOA(757, 22, F7, 3, 41) (dual of [(22, 3), 9, 42]-NRT-code) [i]