MinT - Information on Result #2620064

Information on Result #2620064

Linear OOA(2²⁵⁸, 160, F₂, 3, 74) (dual of [(160, 3), 222, 75]-NRT-code), using strength reduction based on linear OOA(2²⁵⁸, 160, F₂, 3, 75) (dual of [(160, 3), 222, 76]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(8⁴⁶, 40, F₈, 3, 37) (dual of [(40, 3), 74, 38]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8⁴⁶, 45, F₈, 3, 37) (dual of [(45, 3), 89, 38]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,97P) [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		Method
1	Linear OOA(2²⁵⁹, 160, F₂, 3, 74) (dual of [(160, 3), 221, 75]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²⁶⁰, 160, F₂, 3, 74) (dual of [(160, 3), 220, 75]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁵⁸, 80, F₂, 5, 74) (dual of [(80, 5), 142, 75]-NRT-code)	[i]	OOA Folding
4	Linear OOA(2²⁵⁸, 80, F₂, 6, 74) (dual of [(80, 6), 222, 75]-NRT-code)	[i]	OOA Folding