In this paper. we present a new algorithm for fast correlation attacks on stream ciphers with improved cryptanalysis results on the Sosemanuk stream cipher. one of the 7 finalists in the eSTREAM project in 2008. The new algorithm exploits the direct sum construction of covering codes in decoding phase which approximates the random vectors to a nearest codeword in a linear code. https://www.houseandholders.shop/product-category/toothbrush-holder/