首页|The support designs of several families of lifted linear codes
The support designs of several families of lifted linear codes
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NETL
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A generator matrix of a linear code C over GF(q) is also a matrix of the same rank k over any extension field GF(q~ℓ) and generates a linear code of the same length, same dimension and same minimum distance over GF(q~ℓ), denoted by C(q|q~ℓ) and called a lifted code of C. Although C and their lifted codes C(q|q~ℓ) have the same parameters, they have different weight distributions and different applications. Few results about lifted linear codes are known in the literature. This paper proves some fundamental theory for lifted linear codes, and studies the 2-designs of the lifted projective Reed-Muller codes, lifted Hamming codes and lifted Simplex codes. In addition, this paper settles the weight distributions of the lifted Reed-Muller codes of certain orders, and investigates the 3-designs supported by these lifted codes. As a by-product, an infinite family of three-weight projective codes over GF(4) is obtained.
NETL
NSTL
