In this brief paper a quantum algorithm to calculate the Hamming distance of two binary strings of equal length (or messages in theory information) is presented. The algorithm calculates the Hamming weight of two binary strings in one query of an oracle. To calculate the hamming distance of these two strings we only have to calculate the Hamming weight of the xor operation of both strings. To test the algorithms the quantum computer prototype that IBM has given open access to on the cloud has been used to test the results.

We present a method of effectively concealing data in two quantization levels representing blocks based on Absolute Moment Block Truncation Coding (AMBTC) using Hamming code. The reason for choosing AMBTC as the cover media is that AMBTC is not only easily compressible by simple arithmetic operations, but is also efficient for exchanging data in small portable terminals, such as smart devices, because compression efficiency and image quality are satisfactory. AMBTC is expressed in the form of a $trio (a, b, BM)$, where $a$ and $b$ are quantization levels and BM is a bitmap. The quantization level is a pixel value used as a representative value when dividing an image into $4 \times 4$ blocks. Bai \& Chang introduced a method of hiding data using Hamming code. However, this method presented a problem with efficiency compared to the existing methods. In this paper, in order to improve the problem of this method, we minimize the error that occurs when concealing the data using the optimized Hamming code lookup table. We verified that the performance of the proposed method is satisfactory in terms of embedding capacity and quality of the image through sufficient experimental results.

In the era of sustainable development, green supplier selection has become a key component of supply chain management, as it considers criteria such as carbon footprint, water usage, energy usage and recycling capacity. Since the green supplier selection problem involves subjective criteria and uncertainty in preferences, it is well suited to using multi-criteria decision-making methods (MCDM). Although few researchers have investigated MCDM for green supplier selection under uncertainty using intuitionistic and Pythagorean fuzzy sets. Still, the newly developed fermatean fuzzy can handle greater data uncertainty than intuitionistic and Pythagorean fuzzy sets. Since interval extension of fuzzy theory provides more accurate modeling, in this paper, we propose an interval extension of fermatean fuzzy set and discuss its fundamental set operations, arithmetic operations and related properties. We propose the Hamming distance function and the score function of the interval-valued fermatean fuzzy numbers. The recently developed Multi-attribute Border Approximation Area Comparison (MABAC) method is also considered due to its stable and simple computation compared to other conventional MCDM methods. Therefore, an interval-valued fermatean fuzzy MABAC method is proposed and solved to select a green supplier based on multiple criteria. The proposed method's comparative analysis and sensitivity analysis validate the proposed method's effectiveness and robustness.