Let \(\mathbb {F}_{2^{m}}\) be the finite field with 2^m elements, where m is a positive integer. Recently, Heng and Ding in (Finite Fields Appl. 56:308–331, 2019) studied the subfield codes of two families of hyperovel codes and determined the weight distribution of the linear code

for f(x) = x² and f(x) = x⁶ with odd m. Let v₂(⋅) denote the 2-adic order function. This paper investigates more subfield codes of linear codes and obtains the weight distribution of \(\mathcal {C}_{a,b}\) for \(f(x)=x^{2^{i}+2^{j}}\), where i, j are nonnegative integers such that v₂(m) ≤ v₂(i − j)(i ≥ j). In addition to this, we further investigate the punctured code of \(\mathcal {C}_{a,b}\) as follows:

and determine its weight distribution for any nonnegative integers i, j. The parameters of these binary linear codes are new in most cases. Some of the codes and their duals obtained are optimal or almost optimal.

令\（\ mathbb {F} _ {2 ^ {m}} \）是具有2 ^m个元素的有限域，其中m是一个正整数。最近，恒和丁在（有限域申请56：308-331，2019）研究的hyperovel码两个家庭的子场码和确定的线性码的权重分布

对于f（x）= x ²和f（x）= x ⁶（奇数m）。令v ₂（⋅）表示2-adic阶函数。本文研究了线性代码的更多子字段代码，并针对\（f（x）= x ^ {2 ^ {i} + 2 ^ {}获得了\（\ mathcal {C} _ {a，b} \）的权重分布Ĵ}} \） ，其中我，Ĵ为非负整数，使得v ₂（米）≤ v ₂（我- Ĵ）（我≥j）。除此之外，我们进一步研究\（\ mathcal {C} _ {a，b} \）的打孔代码，如下所示：

并确定其对任何非负整数i，j的权重分布。这些二进制线性代码的参数在大多数情况下是新的。获得的某些代码及其对偶是最佳的或几乎最佳的。