MinT - Information on Result #2692081

Information on Result #2692081

Linear OOA(4²²⁵, 538, F₄, 3, 63) (dual of [(538, 3), 1389, 64]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(4²²², 537, F₄, 3, 63) (dual of [(537, 3), 1389, 64]-NRT-code), using

trace code [i] based on linear OOA(64⁷⁴, 179, F₆₄, 3, 63) (dual of [(179, 3), 463, 64]-NRT-code), using
- constructionÂ X applied to AG(3;F,464P) âŠ‚ AG(3;F,469P) [i] based on
  1. linear OOA(64⁷⁰, 176, F₆₄, 3, 63) (dual of [(176, 3), 458, 64]-NRT-code), using algebraic-geometric NRT-code AG(3;F,464P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OOA(64⁶⁵, 176, F₆₄, 3, 58) (dual of [(176, 3), 463, 59]-NRT-code), using algebraic-geometric NRT-code AG(3;F,469P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
  3. linear OOA(64⁴, 3, F₆₄, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64⁴, 64, F₆₄, 3, 4) (dual of [(64, 3), 188, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;188,64) [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(4²²⁶, 538, F₄, 3, 63) (dual of [(538, 3), 1388, 64]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(4²²⁷, 538, F₄, 3, 63) (dual of [(538, 3), 1387, 64]-NRT-code)	[i]		OOA Duplication