Information on Result #1009398

Linear OOA(2249, 2818052, F2, 3, 16) (dual of [(2818052, 3), 8453907, 17]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(265, 21851, F2, 3, 8) (dual of [(21851, 3), 65488, 9]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(265, 65553, F2, 8) (dual of [65553, 65488, 9]-code), using
      • 1 times truncation [i] based on linear OA(266, 65554, F2, 9) (dual of [65554, 65488, 10]-code), using
        • construction X4 applied to Ce(8) ⊂ Ce(6) [i] based on
          1. linear OA(265, 65536, F2, 9) (dual of [65536, 65471, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
          2. linear OA(249, 65536, F2, 7) (dual of [65536, 65487, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
          3. linear OA(217, 18, F2, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,2)), using
          4. linear OA(21, 18, F2, 1) (dual of [18, 17, 2]-code), using
  2. linear OOA(2184, 2796201, F2, 3, 16) (dual of [(2796201, 3), 8388419, 17]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(2184, large, F2, 16) (dual of [large, large−184, 17]-code), using
      • the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OOA(2251, 2818052, F2, 3, 16) (dual of [(2818052, 3), 8453905, 17]-NRT-code) [i]OOA Duplication
2Linear OOA(2249, 1409026, F2, 6, 16) (dual of [(1409026, 6), 8453907, 17]-NRT-code) [i]OOA Folding