Information on Result #700664

Linear OA(2145, 173, F2, 57) (dual of [173, 28, 58]-code), using construction XX applied to C1 = C({0,1,3,5,7,9,11,13,15,19,21,23,27,29,31,63}), C2 = C([0,47]), C3 = C1 + C2 = C([0,31]), and C∩ = C1 ∩ C2 = C({0,1,3,5,7,9,11,13,15,19,21,23,27,29,31,43,47,63}) based on
  1. linear OA(2106, 127, F2, 47) (dual of [127, 21, 48]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,11,13,15,19,21,23,27,29,31,63}, and minimum distance d ≥ |{−4,−3,…,42}|+1 = 48 (BCH-bound) [i]
  2. linear OA(2113, 127, F2, 55) (dual of [127, 14, 56]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [0,47], and designed minimum distance d ≥ |I|+1 = 56 [i]
  3. linear OA(2120, 127, F2, 63) (dual of [127, 7, 64]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,11,13,15,19,21,23,27,29,31,43,47,63}, and minimum distance d ≥ |{0,9,18,…,50}|+1 = 64 (BCH-bound) [i]
  4. linear OA(299, 127, F2, 43) (dual of [127, 28, 44]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [0,42], and designed minimum distance d ≥ |I|+1 = 44 [i]
  5. linear OA(21, 8, F2, 1) (dual of [8, 7, 2]-code), using
  6. linear OA(224, 38, F2, 11) (dual of [38, 14, 12]-code), using

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

None.