MinT - Information on Result #2221745

Information on Result #2221745

Linear OA(2¹⁰³, 159, F₂, 32) (dual of [159, 56, 33]-code), using 1 times truncation based on linear OA(2¹⁰⁴, 160, F₂, 33) (dual of [160, 56, 34]-code), using

concatenation of two codes [i] based on
1. linear OA(16¹⁸, 32, F₁₆, 16) (dual of [32, 14, 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(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(2¹⁰³, 79, F₂, 2, 32) (dual of [(79, 2), 55, 33]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2¹⁰³, 53, F₂, 3, 32) (dual of [(53, 3), 56, 33]-NRT-code)	[i]		OOA Folding