Let be two fixed positive integers, a prime ring with the Martindale qoutient ring , a noncommutative Lie ideal of , and a skew derivation of associated with an automorphism , denoted by <!-- MATH $(\delta ,\varphi )$ --> . If <!-- MATH $[\delta (x), x^m]_k=0$ --> for all , then <!-- MATH $\mathrm {char}(R)=2$ --> and <!-- MATH $R\subseteq M_2(F)$ --> for some field .

Blockchain is a method of recording information that makes it not feasible for the system to be replaced, attacked, or manipulated. A blockchain is equipped with a notebook that copies and processes the various procedures across the network of computers participating in the blockchain. Digital signature algorithm is one of the cryptographic protocols used by the blockchain. In this work, we introduce a new digital signature scheme based on error correcting codes. In the scheme constructed on a [n, k, d]− code over ${𝔽}_q$, which is d ≥ 2t + 1, and the size of the signature length is n − k. The signature verification is based on the bounded distance decoding of the code. Since the verification space is ${{𝔽}_q}^n$, the proposed scheme has an improved performance in terms of working in a wider space.