MinT - Information on Result #2499637

Information on Result #2499637

Linear OOA(4²¹⁵, 544, F₄, 2, 59) (dual of [(544, 2), 873, 60]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(4²¹³, 543, F₄, 2, 59) (dual of [(543, 2), 873, 60]-NRT-code), using

trace code [i] based on linear OOA(64⁷¹, 181, F₆₄, 2, 59) (dual of [(181, 2), 291, 60]-NRT-code), using
- constructionÂ X applied to AG(2;F,292P) âŠ‚ AG(2;F,298P) [i] based on
  1. linear OOA(64⁶⁶, 176, F₆₄, 2, 59) (dual of [(176, 2), 286, 60]-NRT-code), using algebraic-geometric NRT-code AG(2;F,292P) [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(64⁶⁰, 176, F₆₄, 2, 53) (dual of [(176, 2), 292, 54]-NRT-code), using algebraic-geometric NRT-code AG(2;F,298P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
  3. linear OOA(64⁵, 5, F₆₄, 2, 5) (dual of [(5, 2), 5, 6]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64⁵, 64, F₆₄, 2, 5) (dual of [(64, 2), 123, 6]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;123,64) [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(4²¹⁵, 272, F₄, 3, 59) (dual of [(272, 3), 601, 60]-NRT-code)	[i]		OOA Folding