Information on Result #899383

Linear OOA(2543, 4194615, F25, 2, 8) (dual of [(4194615, 2), 8389187, 9]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(257, 314, F25, 2, 4) (dual of [(314, 2), 621, 5]-NRT-code), using
    • OOA 2-folding [i] based on linear OA(257, 628, F25, 4) (dual of [628, 621, 5]-code), using
      • construction XX applied to C1 = C([623,1]), C2 = C([0,2]), C3 = C1 + C2 = C([0,1]), and C∩ = C1 ∩ C2 = C([623,2]) [i] based on
        1. linear OA(255, 624, F25, 3) (dual of [624, 619, 4]-code or 624-cap in PG(4,25)), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,1}, and designed minimum distance d ≥ |I|+1 = 4 [i]
        2. linear OA(255, 624, F25, 3) (dual of [624, 619, 4]-code or 624-cap in PG(4,25)), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 4 [i]
        3. linear OA(257, 624, F25, 4) (dual of [624, 617, 5]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,1,2}, and designed minimum distance d ≥ |I|+1 = 5 [i]
        4. linear OA(253, 624, F25, 2) (dual of [624, 621, 3]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
        5. linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code), using
        6. linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code) (see above)
  2. linear OOA(2536, 4194301, F25, 2, 8) (dual of [(4194301, 2), 8388566, 9]-NRT-code), using

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(2543, 2097307, F25, 10, 8) (dual of [(2097307, 10), 20973027, 9]-NRT-code) [i]OOA Folding and Stacking with Additional Row