MinT - Information on Result #2222749

Information on Result #2222749

Linear OA(2¹¹⁵, 215, F₂, 30) (dual of [215, 100, 31]-code), using 1 times truncation based on linear OA(2¹¹⁶, 216, F₂, 31) (dual of [216, 100, 32]-code), using

concatenation of two codes [i] based on
1. linear OA(32¹⁶, 36, F₃₂, 15) (dual of [36, 20, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(32¹⁶, 43, F₃₂, 15) (dual of [43, 27, 16]-code), using
    - algebraic-geometric code AG(F,27P) [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44, using
      - a function field by SÃ©mirat [i]
2. linear OA(2¹, 6, F₂, 1) (dual of [6, 5, 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, 107, F₂, 2, 30) (dual of [(107, 2), 99, 31]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2¹¹⁵, 71, F₂, 3, 30) (dual of [(71, 3), 98, 31]-NRT-code)	[i]		OOA Folding