MinT - Information on Result #2459892

Information on Result #2459892

Linear OOA(2¹⁸⁷, 109, F₂, 2, 82) (dual of [(109, 2), 31, 83]-NRT-code), using 1 step truncation based on linear OOA(2¹⁸⁸, 110, F₂, 2, 83) (dual of [(110, 2), 32, 84]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16¹⁴, 22, F₁₆, 13) (dual of [22, 8, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(16¹⁴, 24, F₁₆, 13) (dual of [24, 10, 14]-code), using
    - extended algebraic-geometric code AG_e(F,10P) [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, using
      - a function field by SÃ©mirat [i]
2. linear OOA(2⁶, 5, F₂, 2, 5) (dual of [(5, 2), 4, 6]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,4P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
    - an explicitly constructive algebraic function field [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(2¹⁸⁷, 54, F₂, 4, 82) (dual of [(54, 4), 29, 83]-NRT-code)	[i]		OOA Folding