MinT - Information on Result #2425682

Information on Result #2425682

Linear OOA(2²¹⁷, 176, F₂, 2, 68) (dual of [(176, 2), 135, 69]-NRT-code), using strength reduction based on linear OOA(2²¹⁷, 176, F₂, 2, 69) (dual of [(176, 2), 135, 70]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(8⁴³, 44, F₈, 2, 34) (dual of [(44, 2), 45, 35]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8⁴³, 45, F₈, 2, 34) (dual of [(45, 2), 47, 35]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,55P) [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]
2. linear OA(2¹, 4, F₂, 1) (dual of [4, 3, 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(2²¹⁷, 88, F₂, 4, 68) (dual of [(88, 4), 135, 69]-NRT-code)	[i]		OOA Folding