MinT - Information on Result #2243154

Information on Result #2243154

Linear OA(4¹⁶⁵, 327, F₄, 52) (dual of [327, 162, 53]-code), using 1 times truncation based on linear OA(4¹⁶⁶, 328, F₄, 53) (dual of [328, 162, 54]-code), using

concatenation of two codes [i] based on
1. linear OA(64²⁸, 82, F₆₄, 26) (dual of [82, 54, 27]-code), using
  - constructionÂ X applied to AG(F,52P) âŠ‚ AG(F,54P) [i] based on
    1. linear OA(64²⁷, 79, F₆₄, 26) (dual of [79, 52, 27]-code), using algebraic-geometric code AG(F,52P) [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]
    2. linear OA(64²⁵, 79, F₆₄, 24) (dual of [79, 54, 25]-code), using algebraic-geometric code AG(F,54P) [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80 (see above)
    3. linear OA(64¹, 3, F₆₄, 1) (dual of [3, 2, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(64¹, s, F₆₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
2. linear OA(4¹, 4, F₄, 1) (dual of [4, 3, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹, s, F₄, 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		Method
1	Linear OA(4¹⁶⁷, 329, F₄, 52) (dual of [329, 162, 53]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(4¹⁶⁸, 330, F₄, 52) (dual of [330, 162, 53]-code)	[i]	Code Embedding in Larger Space
3	Linear OOA(4¹⁶⁵, 163, F₄, 2, 52) (dual of [(163, 2), 161, 53]-NRT-code)	[i]	OOA Folding