MinT - Information on Result #1444369

Information on Result #1444369

Linear OOA(8⁸⁹, 524306, F₈, 2, 15) (dual of [(524306, 2), 1048523, 16]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(8⁸⁹, 524306, F₈, 15) (dual of [524306, 524217, 16]-code), using

constructionÂ X with VarÅ¡amov bound [i] based on
1. linear OA(8⁸⁸, 524304, F₈, 15) (dual of [524304, 524216, 16]-code), using
  - trace code [i] based on linear OA(64⁴⁴, 262152, F₆₄, 15) (dual of [262152, 262108, 16]-code), using
    - constructionÂ X applied to C([0,7]) âŠ‚ C([0,6]) [i] based on
      1. linear OA(64⁴³, 262145, F₆₄, 15) (dual of [262145, 262102, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145Â | 64⁶âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]
      2. linear OA(64³⁷, 262145, F₆₄, 13) (dual of [262145, 262108, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145Â | 64⁶âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]
      3. linear OA(64¹, 7, F₆₄, 1) (dual of [7, 6, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(64¹, s, F₆₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
2. linear OA(8⁸⁸, 524305, F₈, 14) (dual of [524305, 524217, 15]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 8⁸⁸Â > V_b^sâˆ’1(kâˆ’1)Â = 3519 754360 311078 247598 767231 296367 212708 937478 219662 564852 787360 440423 975191 [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(8⁸⁹, 262153, F₈, 3, 15) (dual of [(262153, 3), 786370, 16]-NRT-code)	[i]		OOA Folding