Information on Result #678205

Linear OA(496, 1048611, F4, 13) (dual of [1048611, 1048515, 14]-code), using construction X applied to Ce(12) ⊂ Ce(8) based on
  1. linear OA(491, 1048576, F4, 13) (dual of [1048576, 1048485, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
  2. linear OA(461, 1048576, F4, 9) (dual of [1048576, 1048515, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
  3. linear OA(45, 35, F4, 3) (dual of [35, 30, 4]-code or 35-cap in PG(4,4)), 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(496, 1048611, F4, 12) (dual of [1048611, 1048515, 13]-code) [i]Strength Reduction
2Linear OA(497, 1048612, F4, 13) (dual of [1048612, 1048515, 14]-code) [i]Code Embedding in Larger Space
3Linear OA(498, 1048613, F4, 13) (dual of [1048613, 1048515, 14]-code) [i]
4Linear OA(499, 1048614, F4, 13) (dual of [1048614, 1048515, 14]-code) [i]
5Linear OA(495, 1048610, F4, 12) (dual of [1048610, 1048515, 13]-code) [i]Truncation
6Linear OA(499, 1048615, F4, 13) (dual of [1048615, 1048516, 14]-code) [i]Construction X with VarÅ¡amov Bound
7Linear OOA(496, 524305, F4, 2, 13) (dual of [(524305, 2), 1048514, 14]-NRT-code) [i]OOA Folding
8Linear OOA(496, 349537, F4, 3, 13) (dual of [(349537, 3), 1048515, 14]-NRT-code) [i]
9Linear OOA(496, 174768, F4, 13, 13) (dual of [(174768, 13), 2271888, 14]-NRT-code) [i]OOA Folding and Stacking with Additional Row