Information on Result #1302748

Linear OA(8114, 262175, F8, 21) (dual of [262175, 262061, 22]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(8113, 262173, F8, 21) (dual of [262173, 262060, 22]-code), using
    • construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
      1. linear OA(8109, 262145, F8, 21) (dual of [262145, 262036, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 812−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
      2. linear OA(885, 262145, F8, 17) (dual of [262145, 262060, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 812−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
      3. linear OA(84, 28, F8, 3) (dual of [28, 24, 4]-code or 28-cap in PG(3,8)), using
  2. linear OA(8113, 262174, F8, 20) (dual of [262174, 262061, 21]-code), using Gilbert–VarÅ¡amov bound and bm = 8113 > Vbs−1(k−1) = 840737 993026 812655 501009 222403 482943 967054 533822 865466 612498 549977 968318 516672 439606 915542 744250 309140 [i]
  3. linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-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(8114, 262175, F8, 2, 21) (dual of [(262175, 2), 524236, 22]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(8114, 262175, F8, 3, 21) (dual of [(262175, 3), 786411, 22]-NRT-code) [i]
3Digital (93, 114, 262175)-net over F8 [i]