Table 1 New QEC MDS codes derived from construction I.

\(10\mid (q-1)\)

20

4

\([[\frac{q^2-1}{4},\frac{q^2-1}{4}-2k,k+1]]_q\)

\(1\le k\le \frac{7(q-1)}{10}\)

\(14\mid (q-1)\)

28

5

\([[\frac{3(q^2-1)}{14},\frac{3(q^2-1)}{14}-2k,k+1]]_q\)

\(1\le k\le \frac{9(q-1)}{14}\)

\(18\mid (q-1)\)

36

7

\([[\frac{2(q^2-1)}{9},\frac{2(q^2-1)}{9}-2k,k+1]]_q\)

\(1\le k\le \frac{2(q-1)}{3}\)

\(22\mid (q-1)\)

44

9

\([[\frac{5(q^2-1)}{22},\frac{5(q^2-1)}{22}-2k,k+1]]_q\)

\(1\le k\le \frac{15(q-1)}{22}\)

\(26\mid (q-1)\)

52

11

\([[\frac{3(q^2-1)}{13},\frac{3(q^2-1)}{13}-2k,k+1]]_q\)

\(1\le k\le \frac{9(q-1)}{13}\)