Information on Result #1301041

Linear OA(4238, 262222, F4, 33) (dual of [262222, 261984, 34]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(4233, 262214, F4, 33) (dual of [262214, 261981, 34]-code), using
    • construction X applied to C([0,16]) ⊂ C([0,12]) [i] based on
      1. linear OA(4217, 262145, F4, 33) (dual of [262145, 261928, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
      2. linear OA(4163, 262145, F4, 25) (dual of [262145, 261982, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
      3. linear OA(416, 69, F4, 7) (dual of [69, 53, 8]-code), using
        • construction XX applied to C1 = C({0,1,2,3,47}), C2 = C([0,5]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,47}) [i] based on
          1. linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,47}, and minimum distance d ≥ |{−1,0,…,4}|+1 = 7 (BCH-bound) [i]
          2. linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
          3. linear OA(416, 63, F4, 7) (dual of [63, 47, 8]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,47}, and minimum distance d ≥ |{−1,0,…,5}|+1 = 8 (BCH-bound) [i]
          4. linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
          5. linear OA(40, 3, F4, 0) (dual of [3, 3, 1]-code), using
          6. linear OA(40, 3, F4, 0) (dual of [3, 3, 1]-code) (see above)
  2. linear OA(4233, 262217, F4, 30) (dual of [262217, 261984, 31]-code), using Gilbert–VarÅ¡amov bound and bm = 4233 > Vbs−1(k−1) = 107 259945 935111 933717 748330 418226 632121 420792 879285 949208 161361 842460 329112 297516 477880 377994 568302 935076 151469 893505 489754 573001 318945 814312 [i]
  3. linear OA(42, 5, F4, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,4)), 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

None.