MinT - Information on Result #2612388

Information on Result #2612388

Linear OOA(2¹³², 84, F₂, 3, 40) (dual of [(84, 3), 120, 41]-NRT-code), using strength reduction based on linear OOA(2¹³², 84, F₂, 3, 41) (dual of [(84, 3), 120, 42]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(8²³, 21, F₈, 3, 20) (dual of [(21, 3), 40, 21]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8²³, 24, F₈, 3, 20) (dual of [(24, 3), 49, 21]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,51P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
      - the Klein quartic over F₈ [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(2¹³³, 84, F₂, 3, 40) (dual of [(84, 3), 119, 41]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹³², 42, F₂, 5, 40) (dual of [(42, 5), 78, 41]-NRT-code)	[i]	OOA Folding
3	Linear OOA(2¹³², 42, F₂, 6, 40) (dual of [(42, 6), 120, 41]-NRT-code)	[i]	OOA Folding