MinT - Information on Result #2224850

Information on Result #2224850

Linear OA(2¹⁸⁹, 221, F₂, 72) (dual of [221, 32, 73]-code), using 3 times truncation based on linear OA(2¹⁹², 224, F₂, 75) (dual of [224, 32, 76]-code), using

concatenation of two codes [i] based on
1. linear OA(16²⁰, 28, F₁₆, 18) (dual of [28, 8, 19]-code), using
  - discarding factors / shortening the dual code based on linear OA(16²⁰, 33, F₁₆, 18) (dual of [33, 13, 19]-code), using
    - extended algebraic-geometric code AG_e(F,14P) [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(2⁴, 8, F₂, 3) (dual of [8, 4, 4]-code or 8-cap in PG(3,2)), using
  - Reedâ€“Muller code RM(1,3) [i]
  - caps in base bÂ =Â 2 [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(2¹⁸⁹, 110, F₂, 2, 72) (dual of [(110, 2), 31, 73]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2¹⁸⁹, 73, F₂, 3, 72) (dual of [(73, 3), 30, 73]-NRT-code)	[i]		OOA Folding