The radiation sensitivity of memory cells increases dramatically as CMOS manufacture technology scales down; therefore, the reliability of memories has become a challenge. 3D technology has gained attention for having several advantages compared to the 2D counterpart, such as high integration density, high performance, low power, and high communication speed. Although several studies are targeting 3D memories, the effects on reliability using this technology have received little attention. This work introduces Line Product Code (LPC), a modified product code-based Error Correction Code (ECC) that uses both Hamming and parity in both rows and columns to implement reliable 3D memories. We implemented two lightweight LPC-based decoding algorithms in interleaved (LPCa-I) and non-interleaved (LPCa) versions, which allowed us to analyze LPC through a set of simulation cases that considers four severity levels of error incidence. The experimental results showed the effectiveness of the LPC-based algorithms, reaching correction rates of up 2.3 times higher compared to other Hamming-based algorithms.