MinT - Information on Result #2670016

Information on Result #2670016

Linear OOA(2¹³², 69, F₂, 3, 48) (dual of [(69, 3), 75, 49]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2¹²⁹, 68, F₂, 3, 48) (dual of [(68, 3), 75, 49]-NRT-code), using

strength reduction [i] based on linear OOA(2¹²⁹, 68, F₂, 3, 49) (dual of [(68, 3), 75, 50]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OOA(8²⁶, 17, F₈, 3, 24) (dual of [(17, 3), 25, 25]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,26P) [i] based on function field F/F₈ with g(F) = 2 and N(F) ≥ 17, using
      - a function field by SÃ©mirat [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(2¹³³, 69, F₂, 3, 48) (dual of [(69, 3), 74, 49]-NRT-code)	[i]		OOA Duplication