MinT - Information on Result #2222155

Information on Result #2222155

Linear OA(2¹¹⁵, 159, F₂, 38) (dual of [159, 44, 39]-code), using 1 times truncation based on linear OA(2¹¹⁶, 160, F₂, 39) (dual of [160, 44, 40]-code), using

concatenation of two codes [i] based on
1. linear OA(16²¹, 32, F₁₆, 19) (dual of [32, 11, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(16²¹, 33, F₁₆, 19) (dual of [33, 12, 20]-code), using
    - extended algebraic-geometric code AG_e(F,13P) [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
      - a function field by SÃ©mirat [i]
2. linear OA(2¹, 5, F₂, 1) (dual of [5, 4, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [i]

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:

	Result		This result only	Method
1	Linear OOA(2¹¹⁵, 53, F₂, 3, 38) (dual of [(53, 3), 44, 39]-NRT-code)	[i]		OOA Folding