MinT - Information on Result #939799

Information on Result #939799

Linear OOA(4²⁵², 567, F₄, 2, 64) (dual of [(567, 2), 882, 65]-NRT-code), using trace code based on linear OOA(64⁸⁴, 189, F₆₄, 2, 64) (dual of [(189, 2), 294, 65]-NRT-code), using

constructionÂ X applied to AG(2;F,287P) âŠ‚ AG(2;F,301P) [i] based on
1. linear OOA(64⁷¹, 176, F₆₄, 2, 64) (dual of [(176, 2), 281, 65]-NRT-code), using algebraic-geometric NRT-code AG(2;F,287P) [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(64⁵⁷, 176, F₆₄, 2, 50) (dual of [(176, 2), 295, 51]-NRT-code), using algebraic-geometric NRT-code AG(2;F,301P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
3. linear OOA(64¹³, 13, F₆₄, 2, 13) (dual of [(13, 2), 13, 14]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(64¹³, 64, F₆₄, 2, 13) (dual of [(64, 2), 115, 14]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;115,64) [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(4²⁵⁴, 568, F₄, 2, 64) (dual of [(568, 2), 882, 65]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
2	Linear OOA(4²⁵³, 567, F₄, 2, 64) (dual of [(567, 2), 881, 65]-NRT-code)	[i]		OOA Duplication