MinT - Information on Result #846044

Information on Result #846044

Linear OOA(8¹⁴², 2063, F₈, 2, 38) (dual of [(2063, 2), 3984, 39]-NRT-code), using OOA 2-folding based on linear OA(8¹⁴², 4126, F₈, 38) (dual of [4126, 3984, 39]-code), using

discarding factors / shortening the dual code based on linear OA(8¹⁴², 4127, F₈, 38) (dual of [4127, 3985, 39]-code), using
- constructionÂ XX applied to C_e(37) âŠ‚ C_e(32) âŠ‚ C_e(30) [i] based on
  1. linear OA(8¹³³, 4096, F₈, 38) (dual of [4096, 3963, 39]-code), using an extension C_e(37) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 8⁴âˆ’1, defining interval IÂ =Â [1,37], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 38 [i]
  2. linear OA(8¹¹³, 4096, F₈, 33) (dual of [4096, 3983, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 8⁴âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
  3. linear OA(8¹⁰⁹, 4096, F₈, 31) (dual of [4096, 3987, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 8⁴âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
  4. linear OA(8⁶, 28, F₈, 4) (dual of [28, 22, 5]-code), using
    - discarding factors / shortening the dual code based on linear OA(8⁶, 56, F₈, 4) (dual of [56, 50, 5]-code), using
      - 1 times truncation [i] based on linear OA(8⁷, 57, F₈, 5) (dual of [57, 50, 6]-code), using
        a code by Danev and Olsson [i]
  5. linear OA(8¹, 3, F₈, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(8¹, 8, F₈, 1) (dual of [8, 7, 2]-code), using
      - Reedâ€“Solomon code RS(7,8) [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

None.