MinT - Information on Result #1554335

Information on Result #1554335

Linear OOA(8⁶⁹, 524296, F₈, 3, 12) (dual of [(524296, 3), 1572819, 13]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(8⁶⁹, 524296, F₈, 12) (dual of [524296, 524227, 13]-code), using

constructionÂ X with VarÅ¡amov bound [i] based on
1. linear OA(8⁶⁸, 524294, F₈, 12) (dual of [524294, 524226, 13]-code), using
  - trace code [i] based on linear OA(64³⁴, 262147, F₆₄, 12) (dual of [262147, 262113, 13]-code), using
    - constructionÂ X applied to C_e(11) âŠ‚ C_e(10) [i] based on
      1. linear OA(64³⁴, 262144, F₆₄, 12) (dual of [262144, 262110, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
      2. linear OA(64³¹, 262144, F₆₄, 11) (dual of [262144, 262113, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
      3. linear OA(64⁰, 3, F₆₄, 0) (dual of [3, 3, 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(8⁶⁸, 524295, F₈, 11) (dual of [524295, 524227, 12]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 8⁶⁸Â > V_b^sâˆ’1(kâˆ’1)Â = 122160 317266 676120 168949 853895 131530 812716 334407 208512 651264 [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(8⁶⁹, 262147, F₈, 15, 12) (dual of [(262147, 15), 3932136, 13]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row