Information on Result #684288

Linear OA(582, 146, F5, 38) (dual of [146, 64, 39]-code), using construction XX applied to Ce(37) ⊂ Ce(31) ⊂ Ce(30) based on
  1. linear OA(574, 125, F5, 38) (dual of [125, 51, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
  2. linear OA(562, 125, F5, 32) (dual of [125, 63, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
  3. linear OA(561, 125, F5, 31) (dual of [125, 64, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
  4. linear OA(57, 20, F5, 5) (dual of [20, 13, 6]-code), using
  5. linear OA(50, 1, F5, 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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(582, 146, F5, 37) (dual of [146, 64, 38]-code) [i]Strength Reduction
2Linear OA(582, 146, F5, 36) (dual of [146, 64, 37]-code) [i]
3Linear OA(584, 148, F5, 38) (dual of [148, 64, 39]-code) [i]Code Embedding in Larger Space
4Linear OA(585, 149, F5, 38) (dual of [149, 64, 39]-code) [i]
5Linear OA(588, 152, F5, 38) (dual of [152, 64, 39]-code) [i]
6Linear OA(581, 145, F5, 37) (dual of [145, 64, 38]-code) [i]Truncation
7Linear OA(580, 144, F5, 36) (dual of [144, 64, 37]-code) [i]
8Linear OA(579, 143, F5, 35) (dual of [143, 64, 36]-code) [i]
9Linear OOA(582, 73, F5, 2, 38) (dual of [(73, 2), 64, 39]-NRT-code) [i]OOA Folding