In general, SAC-OCDMA systems are confronted with many shortcomings that affect their performance, for instance, multiple access interference (MAI), phase-induced intensity noise (PIIN), complex structure, etc. For these purposes, this paper offers a novel technique to design a code based on an identity matrix and shifting feature in order to reduce the aforementioned challenges, namely Identity Column Shift Matrix (ICSM) code. Our proposed code features a zero cross-correlation property (ZCC) which restricts the effect of the MAI, cancels PIIN and thus improves the performance of the SAC-OCDMA system. Furthermore, it simplifies the SAC-OCDMA framework. Mathematical results appear the ability of ICSM code to improve the performance of SAC-OCDMA system as well outperform existing codes such as: Diagonal Permutation Shift (DPS), Dynamic Cyclic Shift (DCS) and Random Diagonal (RD) codes. Secondly, the design of those codes is more complicated than the design of our proposed code. Third, with respect to system capacity, the SAC-OCDMA system based on ICSM, RD, DCS, and DPS codes is 90, 58, 35, and 25 in a row. As a result, the greatest capacity of the system was reached through the use of the ICSM code. On the other side, mimic result demonstrates that our proposed code is suitable for optical communications because meet their requirements through producing BER reaches 10⁻¹³ (<1e-9) and Q-factor reaches 7.2 dB (more than 6 dB).