On Geometric Goppa Codes from Elementary Abelian p-Extensions of $${{\mathbb{F}}}_{{p}^{s}}(x)$$
Nupur Patanker, Sanjay Kumar Singh · Problems of Information Transmission · 2020
Let p be a prime number and s > 0 an integer. In this short note, we investigate one-point geometric Goppa codes associated with an elementary abelian p-extension of $${{\mathbb{F}}}_{{p}^{s}}(x)$$ . We determine their dimension and exact minimum distance in a few cases. These codes are a special case of weak Castle codes. We also list exact values of the second generalized Hamming weight of these codes in a few cases. Simple criteria for self-duality and quasi-self-duality of these codes are also provided. Furthermore, we construct examples of quantum codes, convolutional codes, and locally recoverable codes on the function field.