MinT - Information on Result #940710

Information on Result #940710

Linear OOA(8¹⁶⁸, 1032, F₈, 2, 52) (dual of [(1032, 2), 1896, 53]-NRT-code), using trace code based on linear OOA(64⁸⁴, 516, F₆₄, 2, 52) (dual of [(516, 2), 948, 53]-NRT-code), using

constructionÂ X applied to AG(2;F,971P) âŠ‚ AG(2;F,976P) [i] based on
1. linear OOA(64⁸⁰, 512, F₆₄, 2, 52) (dual of [(512, 2), 944, 53]-NRT-code), using algebraic-geometric NRT-code AG(2;F,971P) [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
  - the Hermitian function field over F₆₄ [i]
2. linear OOA(64⁷⁵, 512, F₆₄, 2, 47) (dual of [(512, 2), 949, 48]-NRT-code), using algebraic-geometric NRT-code AG(2;F,976P) [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513 (see above)
3. linear OOA(64⁴, 4, F₆₄, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(64⁴, 64, F₆₄, 2, 4) (dual of [(64, 2), 124, 5]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;124,64) [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(8¹⁶⁹, 1032, F₈, 2, 52) (dual of [(1032, 2), 1895, 53]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(8¹⁶⁸, 516, F₈, 3, 52) (dual of [(516, 3), 1380, 53]-NRT-code)	[i]		OOA Folding