MinT - Information on Result #1553829

Information on Result #1553829

Linear OOA(8⁴³, 8198, F₈, 3, 11) (dual of [(8198, 3), 24551, 12]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(8⁴³, 8198, F₈, 11) (dual of [8198, 8155, 12]-code), using

constructionÂ X with VarÅ¡amov bound [i] based on
1. linear OA(8⁴², 8196, F₈, 11) (dual of [8196, 8154, 12]-code), using
  - trace code [i] based on linear OA(64²¹, 4098, F₆₄, 11) (dual of [4098, 4077, 12]-code), using
    - constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
      1. linear OA(64²¹, 4096, F₆₄, 11) (dual of [4096, 4075, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
      2. linear OA(64¹⁹, 4096, F₆₄, 10) (dual of [4096, 4077, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
      3. linear OA(64⁰, 2, F₆₄, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(64⁰, s, F₆₄, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
2. linear OA(8⁴², 8197, F₈, 10) (dual of [8197, 8155, 11]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 8⁴²Â > V_b^sâˆ’1(kâˆ’1)Â = 18 479781 192533 737122 457795 483129 121792 [i]
3. linear OA(8⁰, 1, F₈, 0) (dual of [1, 1, 1]-code), using
  - discarding factors / shortening the dual code based on linear OA(8⁰, s, F₈, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
    - OA with only one run / dual of code without redundancy [i]

Mode: 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(8⁴³, 4098, F₈, 15, 11) (dual of [(4098, 15), 61427, 12]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row