MinT - Information on Result #2460131

Information on Result #2460131

Linear OOA(2¹⁵³, 144, F₂, 2, 44) (dual of [(144, 2), 135, 45]-NRT-code), using 1 step truncation based on linear OOA(2¹⁵⁴, 145, F₂, 2, 45) (dual of [(145, 2), 136, 46]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(16²⁴, 29, F₁₆, 2, 22) (dual of [(29, 2), 34, 23]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(16²⁴, 33, F₁₆, 2, 22) (dual of [(33, 2), 42, 23]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,43P) [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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2¹⁵³, 72, F₂, 4, 44) (dual of [(72, 4), 135, 45]-NRT-code)	[i]		OOA Folding