MinT - Information on Result #1546586

Information on Result #1546586

Linear OOA(4²⁵⁷, 1767675, F₄, 3, 30) (dual of [(1767675, 3), 5302768, 31]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4²⁵⁷, 1767675, F₄, 2, 30) (dual of [(1767675, 2), 3535093, 31]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4²⁵⁷, 2097186, F₄, 2, 30) (dual of [(2097186, 2), 4194115, 31]-NRT-code), using
- 4¹ times duplication [i] based on linear OOA(4²⁵⁶, 2097186, F₄, 2, 30) (dual of [(2097186, 2), 4194116, 31]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(4²⁵⁶, 4194372, F₄, 30) (dual of [4194372, 4194116, 31]-code), using
    - constructionÂ X applied to C_e(29) âŠ‚ C_e(22) [i] based on
      1. linear OA(4²⁴³, 4194304, F₄, 30) (dual of [4194304, 4194061, 31]-code), using an extension C_e(29) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,29], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
      2. linear OA(4¹⁸⁸, 4194304, F₄, 23) (dual of [4194304, 4194116, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
      3. linear OA(4¹³, 68, F₄, 6) (dual of [68, 55, 7]-code), using
        discarding factors / shortening the dual code based on linear OA(4¹³, 70, F₄, 6) (dual of [70, 57, 7]-code), using
        generator matrices provided on Edelâ€™s homepage [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(4²⁵⁷, 353534, F₄, 33, 30) (dual of [(353534, 33), 11666365, 31]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row