MinT - Information on Result #1324104

Information on Result #1324104

Linear OA(4²¹⁶, 16453, F₄, 38) (dual of [16453, 16237, 39]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(4²¹⁵, 16451, F₄, 38) (dual of [16451, 16236, 39]-code), using
- constructionÂ X applied to C_e(37) âŠ‚ C_e(28) [i] based on
  1. linear OA(4¹⁹⁷, 16384, F₄, 38) (dual of [16384, 16187, 39]-code), using an extension C_e(37) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 4⁷âˆ’1, defining interval IÂ =Â [1,37], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 38 [i]
  2. linear OA(4¹⁴⁸, 16384, F₄, 29) (dual of [16384, 16236, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 4⁷âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
  3. linear OA(4¹⁸, 67, F₄, 8) (dual of [67, 49, 9]-code), using
    - discarding factors / shortening the dual code based on linear OA(4¹⁸, 68, F₄, 8) (dual of [68, 50, 9]-code), using
      - a code from Grasslâ€™s database [i]
linear OA(4²¹⁵, 16452, F₄, 37) (dual of [16452, 16237, 38]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 4²¹⁵Â > V_b^sâˆ’1(kâˆ’1)Â = 23 573657 126516 550663 491782 658670 762352 248556 076389 724402 882582 868695 140782 739104 324904 495368 479772 912485 429111 101385 092733 537200 [i]
linear OA(4⁰, 1, F₄, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(4⁰, s, F₄, 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		Method
1	Linear OOA(4²¹⁶, 16453, F₄, 2, 38) (dual of [(16453, 2), 32690, 39]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(4²¹⁶, 16453, F₄, 3, 38) (dual of [(16453, 3), 49143, 39]-NRT-code)	[i]
3	Digital (178, 216, 16453)-net over F₄	[i]