MinT - Information on Result #2251716

Information on Result #2251716

Linear OA(8¹⁷¹, 251, F₈, 82) (dual of [251, 80, 83]-code), using 1 times truncation based on linear OA(8¹⁷², 252, F₈, 83) (dual of [252, 80, 84]-code), using

concatenation of two codes [i] based on
1. linear OA(64⁴⁴, 84, F₆₄, 41) (dual of [84, 40, 42]-code), using
  - discarding factors / shortening the dual code based on linear OA(64⁴⁴, 103, F₆₄, 41) (dual of [103, 59, 42]-code), using
    - algebraic-geometric code AG(F,61P) [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]
2. linear OA(8¹, 3, F₈, 1) (dual of [3, 2, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(8¹, s, F₈, 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(8¹⁷¹, 125, F₈, 2, 82) (dual of [(125, 2), 79, 83]-NRT-code)	[i]		OOA Folding