Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Inspired by the recent work on binary cyclic codes published in IEEE Trans. Inf. Theory, vol. 68, no. 12, pp. 7842-7849, 2022, the objectives of this paper are the construction and analyses of five infinite families of binary cyclic codes with parameters $[n, k]$ and $(n-6)/3 \leq k \leq 2(n+6)/3$. Three of the five families of binary cyclic codes and their duals have a very good lower bound on their minimum distances and contain distance-optimal codes. The other two families of binary cyclic codes are composed of binary duadic codes with a square-root-like lower bound on their minimum distances. As a by-product, two infinite families of self-dual binary codes with a square-root-like lower bound on their minimum distances are obtained.
翻译:Cyclic代码是一种有趣的线性代码类型,由于其高效编码和解码算法,在通信和储存系统中具有广泛的应用。受到最近在IEEE Trans上公布的双环代码工作启发。Inf. Theory, vol. 68, no.12, pp. 7842-7849, 2022, 本文的目标是构建和分析五个双环代码的无限家庭,其参数为 $n, k]$和 $(n-6)/3\leq k k\leq 2(n+6)/3 。五个双环代码家庭中,有三个家庭在最低距离上限制非常低,并含有距离最理想的代码。其他两个双环代码由二元双环代码组成,其最小距离上绑定的距离要小于平底线。作为副产品,获得两个自己二元二元代码的无限家庭,其最低距离限制为平底。