Profile: Mark Mattson

An Assmus-Mattson theorem for Z4-codes

The Assmus{Mattson theorem is a method to nd designs in linear codes over a nite eld. The purpose of this paper is to give an analogue of this theorem for Z 4 -codes by using the harmonic weight enumerator which is introduced by Bachoc. This theorem can nd some 5-designs in the lifted Golay code over Z 4 which were discovered previously by other methods. Index Terms { Z 4 -codes, Assmus{Mattson...

A strengthening of the Assmus-Mattson theorem

Let w 1 = d, w 2 , ... , w s be the weights of the nonzero codewords in a binary linear [n , k, d] code C, and let w1′ , w2′ , ... , ws ′ ′ be the nonzero weights in the dual code C ⊥ . Let t be an integer in the range 0 < t < d such that there are at most d − t weights wi′ with 0 < wi′ ≤ n − t. Assmus and Mattson proved that the words of any weight w i in C form a t-design. We show that if w 2...

فرایند دریافت E- Mark

با گسترش روزافزون صنعت حمل‌و‌نقل درجهان و ارتقای استانداردها، تدوین و اجرای استانداردهای بین‌المللی، یک امر ضروری به‌نظر می‌رسد. E- Mark یک مجموعه قانون‌های هماهنگ بین‌المللی برای خودرو و قطعه‌های آن است که تمامی تولیدکنندگان وسیله‌های نقیله و قطعه‌ها ملزم به رعایت آن هستند. تولیدکنندگان تایر نیز از این امر مستثنی نیستند و باید برای تایرهای خود این مجوز را دریافت کنند. در این مقاله روش دریافت E...

An Assmus-Mattson theorem for codes over commutative association schemes

Idempotents, Mattson-Solomon Polynomials and Binary LDPC codes

We show how to construct an algorithm to search for binary idempotents which may be used to construct binary LDPC codes. The algorithm, which allows control of the key properties of sparseness, code rate and minimum distance, is constructed in the Mattson-Solomon domain. Some of the new codes, found by using this technique, are displayed.