Information on Result #702802

Linear OA(2153, 1075, F2, 29) (dual of [1075, 922, 30]-code), using construction XX applied to C1 = C([1019,20]), C2 = C([0,24]), C3 = C1 + C2 = C([0,20]), and C∩ = C1 ∩ C2 = C([1019,24]) based on
  1. linear OA(2121, 1023, F2, 25) (dual of [1023, 902, 26]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,20}, and designed minimum distance d ≥ |I|+1 = 26 [i]
  2. linear OA(2121, 1023, F2, 25) (dual of [1023, 902, 26]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,24], and designed minimum distance d ≥ |I|+1 = 26 [i]
  3. linear OA(2141, 1023, F2, 29) (dual of [1023, 882, 30]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,24}, and designed minimum distance d ≥ |I|+1 = 30 [i]
  4. linear OA(2101, 1023, F2, 21) (dual of [1023, 922, 22]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
  5. linear OA(26, 26, F2, 3) (dual of [26, 20, 4]-code or 26-cap in PG(5,2)), using
  6. linear OA(26, 26, F2, 3) (dual of [26, 20, 4]-code or 26-cap in PG(5,2)) (see above)

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(2152, 1074, F2, 28) (dual of [1074, 922, 29]-code) [i]Truncation
2Linear OOA(2153, 537, F2, 2, 29) (dual of [(537, 2), 921, 30]-NRT-code) [i]OOA Folding
3Linear OOA(2153, 358, F2, 3, 29) (dual of [(358, 3), 921, 30]-NRT-code) [i]
4Linear OOA(2153, 268, F2, 4, 29) (dual of [(268, 4), 919, 30]-NRT-code) [i]
5Linear OOA(2153, 215, F2, 5, 29) (dual of [(215, 5), 922, 30]-NRT-code) [i]
6Linear OOA(2153, 179, F2, 6, 29) (dual of [(179, 6), 921, 30]-NRT-code) [i]
7Linear OOA(2153, 153, F2, 7, 29) (dual of [(153, 7), 918, 30]-NRT-code) [i]
8Linear OOA(2153, 134, F2, 8, 29) (dual of [(134, 8), 919, 30]-NRT-code) [i]