MinT - Information on Result #1304037

Information on Result #1304037

Linear OA(2²¹¹, 342, F₂, 56) (dual of [342, 131, 57]-code), using 3 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (3, 1, 1) based on linear OA(2²⁰⁶, 334, F₂, 56) (dual of [334, 128, 57]-code), using

1 times truncation [i] based on linear OA(2²⁰⁷, 335, F₂, 57) (dual of [335, 128, 58]-code), using
- concatenation of two codes [i] based on
  1. linear OA(16³⁵, 67, F₁₆, 28) (dual of [67, 32, 29]-code), using
    - constructionÂ X applied to AG(F,35P) âŠ‚ AG(F,37P) [i] based on
      1. linear OA(16³⁴, 64, F₁₆, 28) (dual of [64, 30, 29]-code), using algebraic-geometric code AG(F,35P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
        the Hermitian function field over F₁₆ [i]
      2. linear OA(16³², 64, F₁₆, 26) (dual of [64, 32, 27]-code), using algebraic-geometric code AG(F,37P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
      3. linear OA(16¹, 3, F₁₆, 1) (dual of [3, 2, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(16¹, s, F₁₆, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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: 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 OA(2²¹², 343, F₂, 57) (dual of [343, 131, 58]-code)	[i]		Adding a Parity Check Bit