MinT - Information on Result #1443470

Information on Result #1443470

Linear OOA(8⁵³, 8206, F₈, 2, 13) (dual of [(8206, 2), 16359, 14]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(8⁵³, 8206, F₈, 13) (dual of [8206, 8153, 14]-code), using

constructionÂ X with VarÅ¡amov bound [i] based on
1. linear OA(8⁵², 8204, F₈, 13) (dual of [8204, 8152, 14]-code), using
  - trace code [i] based on linear OA(64²⁶, 4102, F₆₄, 13) (dual of [4102, 4076, 14]-code), using
    - constructionÂ X applied to C([0,6]) âŠ‚ C([0,5]) [i] based on
      1. linear OA(64²⁵, 4097, F₆₄, 13) (dual of [4097, 4072, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097Â | 64⁴âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]
      2. linear OA(64²¹, 4097, F₆₄, 11) (dual of [4097, 4076, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097Â | 64⁴âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]
      3. linear OA(64¹, 5, F₆₄, 1) (dual of [5, 4, 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(8⁵², 8205, F₈, 12) (dual of [8205, 8153, 13]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 8⁵²Â > V_b^sâˆ’1(kâˆ’1)Â = 557 667598 560624 431571 643600 935683 193596 222431 [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(8⁵³, 4103, F₈, 3, 13) (dual of [(4103, 3), 12256, 14]-NRT-code)	[i]		OOA Folding