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I T ] 1 2 O ct 2 01 9 Two classes of pary linear codes and their duals ∗
| Content Provider | Semantic Scholar |
|---|---|
| Author | Wang, Xiaoqiang Zheng, Dabin Zhang, Yunfan |
| Copyright Year | 2019 |
| Abstract | Let Fpm be the finite field of order p , where p is an odd prime and m is a positive integer. In this paper, we investigate a class of subfield codes of linear codes and obtain the weight distribution of Ck = {(( Trm1 ( ax +1 + bx ) + c ) x∈Fpm ,Trm1 (a) ) : a, b ∈ Fpm , c ∈ Fp } , where k is a nonnegative integer. Our results generalize the results of the subfield codes of the conic codes in [19]. Among other results, we study the punctured code of Ck, which is defined as C̄k = {( Trm1 ( ax +1 + bx ) + c ) x∈Fpm : a, b ∈ Fpm , c ∈ Fp } . The parameters of these linear codes are new in some cases. Some of the presented codes are optimal or almost optimal. Moreover, let v2(·) denote the 2-adic order function and v2(0) = ∞, the duals of Ck and C̄k are optimal with respect to the Sphere Packing bound if p > 3, and the dual of C̄k is an optimal ternary linear code for the case v2(m) ≤ v2(k) if p = 3 and m > 1. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://export.arxiv.org/pdf/1910.05461 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
