MinT - Information on Result #939717

Information on Result #939717

Linear OOA(4²²⁸, 561, F₄, 2, 58) (dual of [(561, 2), 894, 59]-NRT-code), using trace code based on linear OOA(64⁷⁶, 187, F₆₄, 2, 58) (dual of [(187, 2), 298, 59]-NRT-code), using

constructionÂ X applied to AG(2;F,293P) âŠ‚ AG(2;F,305P) [i] based on
1. linear OOA(64⁶⁵, 176, F₆₄, 2, 58) (dual of [(176, 2), 287, 59]-NRT-code), using algebraic-geometric NRT-code AG(2;F,293P) [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(64⁵³, 176, F₆₄, 2, 46) (dual of [(176, 2), 299, 47]-NRT-code), using algebraic-geometric NRT-code AG(2;F,305P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
3. linear OOA(64¹¹, 11, F₆₄, 2, 11) (dual of [(11, 2), 11, 12]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(64¹¹, 64, F₆₄, 2, 11) (dual of [(64, 2), 117, 12]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;117,64) [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(4²³⁰, 562, F₄, 2, 58) (dual of [(562, 2), 894, 59]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
2	Linear OOA(4²²⁹, 561, F₄, 2, 58) (dual of [(561, 2), 893, 59]-NRT-code)	[i]		OOA Duplication