MinT - Information on Result #1304080

Information on Result #1304080

Linear OA(2²⁴¹, 352, F₂, 68) (dual of [352, 111, 69]-code), using 3 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (3, 1, 1) based on linear OA(2²³⁶, 344, F₂, 68) (dual of [344, 108, 69]-code), using

1 times truncation [i] based on linear OA(2²³⁷, 345, F₂, 69) (dual of [345, 108, 70]-code), using
- concatenation of two codes [i] based on
  1. linear OA(16⁴², 69, F₁₆, 34) (dual of [69, 27, 35]-code), using
    - constructionÂ X applied to AG(F,29P) âŠ‚ AG(F,32P) [i] based on
      1. linear OA(16⁴⁰, 64, F₁₆, 34) (dual of [64, 24, 35]-code), using algebraic-geometric code AG(F,29P) [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(16³⁷, 64, F₁₆, 31) (dual of [64, 27, 32]-code), using algebraic-geometric code AG(F,32P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
      3. linear OA(16², 5, F₁₆, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,16)), using
        discarding factors / shortening the dual code based on linear OA(16², 16, F₁₆, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
        Reedâ€“Solomon code RS(14,16) [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(2²⁴², 353, F₂, 69) (dual of [353, 111, 70]-code)	[i]		Adding a Parity Check Bit