Information on Result #737302

Linear OA(4177, 4165, F4, 35) (dual of [4165, 3988, 36]-code), using construction X applied to C([0,17]) ⊂ C([0,12]) based on
  1. linear OA(4157, 4097, F4, 35) (dual of [4097, 3940, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (BCH-bound) [i]
  2. linear OA(4109, 4097, F4, 25) (dual of [4097, 3988, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
  3. linear OA(420, 68, F4, 9) (dual of [68, 48, 10]-code), using
    • construction X applied to Ce(8) ⊂ Ce(6) [i] based on
      1. linear OA(419, 64, F4, 9) (dual of [64, 45, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
      2. linear OA(416, 64, F4, 7) (dual of [64, 48, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
      3. linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-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(4178, 4166, F4, 35) (dual of [4166, 3988, 36]-code) [i]Code Embedding in Larger Space
2Linear OA(4180, 4168, F4, 35) (dual of [4168, 3988, 36]-code) [i]
3Linear OA(4181, 4169, F4, 35) (dual of [4169, 3988, 36]-code) [i]
4Linear OOA(4177, 2082, F4, 2, 35) (dual of [(2082, 2), 3987, 36]-NRT-code) [i]OOA Folding
5Linear OOA(4177, 1388, F4, 3, 35) (dual of [(1388, 3), 3987, 36]-NRT-code) [i]