On the Minimum Distance of Some Improper Array Codes

抄録

For an odd prime q and an integer m≤q, we can construct a regular quasi-cyclic parity-check matrix H_I(m,q) that specifies a linear block code C_I(m,q), called an improper array code. In this letter, we prove the minimum distance of C_I(4,q) is equal to 10 for any q≥11. In addition, we prove the minimum distance of C_I(5,q) is upper bounded by 12 for any q≥11 and conjecture the upper bound is tight.