MinT - Information on Result #2225513

Information on Result #2225513

Linear OA(2¹⁹³, 245, F₂, 64) (dual of [245, 52, 65]-code), using 3 times truncation based on linear OA(2¹⁹⁶, 248, F₂, 67) (dual of [248, 52, 68]-code), using

concatenation of two codes [i] based on
1. linear OA(16¹⁸, 31, F₁₆, 16) (dual of [31, 13, 17]-code), using
  - discarding factors / shortening the dual code based on linear OA(16¹⁸, 33, F₁₆, 16) (dual of [33, 15, 17]-code), using
    - extended algebraic-geometric code AG_e(F,16P) [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(2¹⁹³, 122, F₂, 2, 64) (dual of [(122, 2), 51, 65]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2¹⁹³, 81, F₂, 3, 64) (dual of [(81, 3), 50, 65]-NRT-code)	[i]		OOA Folding