MinT - Information on Result #2482200

Information on Result #2482200

Linear OOA(2²⁴³, 227, F₂, 2, 67) (dual of [(227, 2), 211, 68]-NRT-code), using 2¹ times duplication based on linear OOA(2²⁴², 227, F₂, 2, 67) (dual of [(227, 2), 212, 68]-NRT-code), using

2 times NRT-code embedding in larger space [i] based on linear OOA(2²³⁸, 225, F₂, 2, 67) (dual of [(225, 2), 212, 68]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OOA(16³⁷, 45, F₁₆, 2, 33) (dual of [(45, 2), 53, 34]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,56P) [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
      - a function field by GarcÃa and Quoos [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

None.