Information on Result #1014356

Linear OOA(8104, 6640986, F8, 3, 10) (dual of [(6640986, 3), 19922854, 11]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(830, 1048584, F8, 3, 5) (dual of [(1048584, 3), 3145722, 6]-NRT-code), using
    • OOA 2-folding and stacking with additional row [i] based on linear OA(830, 2097169, F8, 5) (dual of [2097169, 2097139, 6]-code), using
      • construction X4 applied to C([0,2]) ⊂ C([0,1]) [i] based on
        1. linear OA(829, 2097153, F8, 5) (dual of [2097153, 2097124, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
        2. linear OA(815, 2097153, F8, 3) (dual of [2097153, 2097138, 4]-code or 2097153-cap in PG(14,8)), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,1], and minimum distance d ≥ |{−1,0,1}|+1 = 4 (BCH-bound) [i]
        3. linear OA(815, 16, F8, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,8)), using
        4. linear OA(81, 16, F8, 1) (dual of [16, 15, 2]-code), using
  2. linear OOA(874, 5592402, F8, 3, 10) (dual of [(5592402, 3), 16777132, 11]-NRT-code), using
    • trace code [i] based on linear OOA(6437, 2796201, F64, 3, 10) (dual of [(2796201, 3), 8388566, 11]-NRT-code), using
      • OOA 3-folding [i] based on linear OA(6437, large, F64, 10) (dual of [large, large−37, 11]-code), using
        • the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [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(8104, 3320492, F8, 15, 10) (dual of [(3320492, 15), 49807276, 11]-NRT-code) [i]OOA Folding and Stacking with Additional Row