MinT - Information on Result #2226200

Information on Result #2226200

Linear OA(2²⁵³, 281, F₂, 105) (dual of [281, 28, 106]-code), using 2 times truncation based on linear OA(2²⁵⁵, 283, F₂, 107) (dual of [283, 28, 108]-code), using

constructionÂ X applied to C_e(110) âŠ‚ C_e(94) [i] based on
1. linear OA(2²³⁵, 256, F₂, 111) (dual of [256, 21, 112]-code), using an extension C_e(110) of the primitive narrow-sense BCH-code C(I) with length 255Â = 2⁸âˆ’1, defining interval IÂ =Â [1,110], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 111 [i]
2. linear OA(2²²⁷, 256, F₂, 95) (dual of [256, 29, 96]-code), using an extension C_e(94) of the primitive narrow-sense BCH-code C(I) with length 255Â = 2⁸âˆ’1, defining interval IÂ =Â [1,94], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 95 [i]
3. linear OA(2²⁰, 27, F₂, 11) (dual of [27, 7, 12]-code), using
  - residual code [i] based on linear OA(2⁴³, 51, F₂, 23) (dual of [51, 8, 24]-code), using
    - concatenation of two codes [i] based on
      1. linear OA(4¹³, 17, F₄, 11) (dual of [17, 4, 12]-code), using
        projective code from ovoid in PG(3,Â 4) [i]
      2. linear OA(2¹, 3, F₂, 1) (dual of [3, 2, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]

Mode: Constructive and 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(2²⁵³, 140, F₂, 2, 105) (dual of [(140, 2), 27, 106]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²⁵³, 56, F₂, 5, 105) (dual of [(56, 5), 27, 106]-NRT-code)	[i]		OOA Folding