MinT - Information on Result #2418823

Information on Result #2418823

Linear OOA(2¹¹², 110, F₂, 2, 32) (dual of [(110, 2), 108, 33]-NRT-code), using strength reduction based on linear OOA(2¹¹², 110, F₂, 2, 33) (dual of [(110, 2), 108, 34]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(16¹⁷, 22, F₁₆, 2, 16) (dual of [(22, 2), 27, 17]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(16¹⁷, 24, F₁₆, 2, 16) (dual of [(24, 2), 31, 17]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,31P) [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 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(2¹¹², 55, F₂, 4, 32) (dual of [(55, 4), 108, 33]-NRT-code)	[i]		OOA Folding