Information on Result #700616

Linear OA(273, 143, F2, 23) (dual of [143, 70, 24]-code), using construction XX applied to C1 = C({0,1,3,5,7,9,11,13,15,63}), C2 = C([0,19]), C3 = C1 + C2 = C([0,15]), and C∩ = C1 ∩ C2 = C({0,1,3,5,7,9,11,13,15,19,63}) based on
  1. linear OA(264, 127, F2, 21) (dual of [127, 63, 22]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,11,13,15,63}, and minimum distance d ≥ |{−2,−1,…,18}|+1 = 22 (BCH-bound) [i]
  2. linear OA(264, 127, F2, 21) (dual of [127, 63, 22]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 22 [i]
  3. linear OA(271, 127, F2, 23) (dual of [127, 56, 24]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,11,13,15,19,63}, and minimum distance d ≥ |{−2,−1,…,20}|+1 = 24 (BCH-bound) [i]
  4. linear OA(257, 127, F2, 19) (dual of [127, 70, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 20 [i]
  5. linear OA(21, 8, F2, 1) (dual of [8, 7, 2]-code), using
  6. linear OA(21, 8, F2, 1) (dual of [8, 7, 2]-code) (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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(272, 142, F2, 22) (dual of [142, 70, 23]-code) [i]Truncation
2Linear OA(279, 151, F2, 22) (dual of [151, 72, 23]-code) [i]Construction X with VarÅ¡amov Bound
3Linear OOA(273, 71, F2, 2, 23) (dual of [(71, 2), 69, 24]-NRT-code) [i]OOA Folding
4Linear OOA(273, 47, F2, 3, 23) (dual of [(47, 3), 68, 24]-NRT-code) [i]