MinT - Information on Result #939674

Information on Result #939674

Linear OOA(4²¹³, 558, F₄, 2, 54) (dual of [(558, 2), 903, 55]-NRT-code), using trace code based on linear OOA(64⁷¹, 186, F₆₄, 2, 54) (dual of [(186, 2), 301, 55]-NRT-code), using

constructionÂ X applied to AG(2;F,297P) âŠ‚ AG(2;F,308P) [i] based on
1. linear OOA(64⁶¹, 176, F₆₄, 2, 54) (dual of [(176, 2), 291, 55]-NRT-code), using algebraic-geometric NRT-code AG(2;F,297P) [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(64⁵⁰, 176, F₆₄, 2, 43) (dual of [(176, 2), 302, 44]-NRT-code), using algebraic-geometric NRT-code AG(2;F,308P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
3. linear OOA(64¹⁰, 10, F₆₄, 2, 10) (dual of [(10, 2), 10, 11]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(64¹⁰, 64, F₆₄, 2, 10) (dual of [(64, 2), 118, 11]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;118,64) [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, 559, F₄, 2, 54) (dual of [(559, 2), 903, 55]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
2	Linear OOA(4²¹⁴, 558, F₄, 2, 54) (dual of [(558, 2), 902, 55]-NRT-code)	[i]		OOA Duplication