MinT - Information on Result #1564154

Information on Result #1564154

Linear OOA(64²⁴, 1708, F₆₄, 3, 12) (dual of [(1708, 3), 5100, 13]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(64²⁴, 1708, F₆₄, 2, 12) (dual of [(1708, 2), 3392, 13]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(64²⁴, 2050, F₆₄, 2, 12) (dual of [(2050, 2), 4076, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(64²⁴, 4100, F₆₄, 12) (dual of [4100, 4076, 13]-code), using
  - discarding factors / shortening the dual code based on linear OA(64²⁴, 4101, F₆₄, 12) (dual of [4101, 4077, 13]-code), using
    - constructionÂ X applied to C_e(11) âŠ‚ C_e(9) [i] based on
      1. linear OA(64²³, 4096, F₆₄, 12) (dual of [4096, 4073, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [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(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]

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(64²⁴, 853, F₆₄, 15, 12) (dual of [(853, 15), 12771, 13]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row