Splitting sums of binary polynomials

Key Points

• The aim is to explore conditions under which sums of binary polynomials have specific forms.
• Analyzed sums of distinct polynomials over the ring of binary polynomials.
• Established criteria for forms of polynomial sums in the context of B_2[x].
• Proved certain properties through algebraic methods.
• Proved that m = 5 is the minimal number for distinct polynomials.
• Showed that sums cannot all be in the form x^k(x+1)^{B1}.