Information on Result #1299963

Linear OA(488, 262178, F4, 12) (dual of [262178, 262090, 13]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(486, 262175, F4, 12) (dual of [262175, 262089, 13]-code), using
    • 1 times truncation [i] based on linear OA(487, 262176, F4, 13) (dual of [262176, 262089, 14]-code), using
      • construction X applied to Ce(12) ⊂ Ce(8) [i] based on
        1. linear OA(482, 262144, F4, 13) (dual of [262144, 262062, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
        2. linear OA(455, 262144, F4, 9) (dual of [262144, 262089, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
        3. linear OA(45, 32, F4, 3) (dual of [32, 27, 4]-code or 32-cap in PG(4,4)), using
  2. linear OA(486, 262176, F4, 10) (dual of [262176, 262090, 11]-code), using Gilbert–VarÅ¡amov bound and bm = 486 > Vbs−1(k−1) = 317391 348499 115803 012495 448944 882986 828411 850606 [i]
  3. linear OA(41, 2, F4, 1) (dual of [2, 1, 2]-code), using

Mode: 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 OOA(488, 131089, F4, 2, 12) (dual of [(131089, 2), 262090, 13]-NRT-code) [i]OOA Folding